2020
17
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1

Use of the Shearlet Transform and Transfer Learning in Offline Handwritten Signature Verification and Recognition
https://scma.maragheh.ac.ir/article_38395.html
10.22130/scma.2019.99098.536
1
Despite the growing growth of technology, handwritten signature has been selected as the first option between biometrics by users. In this paper, a new methodology for offline handwritten signature verification and recognition based on the Shearlet transform and transfer learning is proposed. Since, a large percentage of handwritten signatures are composed of curves and the performance of a signature verification/recognition system is directly related to the edge structures, subbands of shearlet transform of signature images are good candidates for input information to the system. Furthermore, by using transfer learning of some pretrained models, appropriate features would be extracted. In this study, four pretrained models have been used: SigNet and SigNetF (trained on offline signature datasets), VGG16 and VGG19 (trained on ImageNet dataset). Experiments have been conducted using three datasets: UTSig, FUMPHSD and MCYT75. Obtained experimental results, in comparison with the literature, verify the effectiveness of the presented method in both signature verification and signature recognition.
0

1
31


Atefeh
Foroozandeh
Department of Applied Mathematics, Faculty of Sciences and Modern Technology, Graduate University of Advanced Technology, Kerman, Iran.
Iran
atforoozandeh@yahoo.com


Ataollah
Askari Hemmat
Department of Applied Mathematics, Faculty of
Mathematics and Computer, Shahid Bahonar University of Kerman,
Kerman, Iran.
Iran
askari@uk.ac.ir


Hossein
Rabbani
Department of Biomedical Engineering, School of Advanced Technologies in Medicine,
Isfahan University of Medical Sciences, Isfahan, Iran.
Iran
h_rabbanimed@mui.ac.ir
Offline handwritten signature
Signature verification
Signature recognition
Shearlet transform
Transfer learning
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(IJBB), 5 (2011), pp. 234248.##[65] K. Simonyan and A. Zisserman, Very deep convolutional networks for largescale image recognition, arXiv 1409.1556, 2014.##[66] A. Soleimani, B.N. Araabi and K. Fouladi, Deep multitask metric learning for offline signature verification, Pattern Recognit. Lett., 80 (2016), pp. 8490.##[67] A. Soleimani, K. Fouladi and B.N. Araabi, UTSig: a Persian offline signature database, IET Biometrics, 6 (2017), pp. 18.##[68] A. Soleimani, K. Fouladi and B.N. Araabi, Persian offline signature verification based on curvature and gradient histograms, 6th Int. Conf. Comput. Knowledge Eng., (2016), pp. 147152.##[69] H. Srinivasan, S.N. Srihari and M.J. Beal, Machine learning for signature verification, Computer Vision, Graphics and Image Processing, Springer Berlin Heidelberg, (2006), pp. 761775.##[70] J.L. Starck, F. Murtagh and J. 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Ghasemi, Online signature verification using doublestage feature extraction modelled by dynamic feature stability experiment, IET Biometrics, 6 (2017), pp. 393401.##[76] F.Yuan, LM. Po, M. Liu, X, Xu, W. Jian, K. Wong and K. Cheung, Shearlet based video fingerprint for contentbased copy detection, J. Signal Inf. Process., 7 (2016), pp. 8497.##[77] G. Zaccone, M.R. Karim and Menshawy, Deep learning with TensorFlow, explore neural networks and build intelligent systems with Python, Birmingham, England, Mumbai, India, Packt, 2017.##[78] G. Zhong, L. Wang and J. Dong, An overview on data representation learning: from traditional feature learning to recent deep learning, J. Financ Data Sci., 2 (2016), pp. 265278.##[79] E.N. Zois, L. Alewijnse and G. Economou, Offline signature verification and quality characterization using posetoriented grid features, Pattern Recognit., 54 (2016), pp. 162177.##]
1

Weighted Composition Operators Between Extended Lipschitz Algebras on Compact Metric Spaces
https://scma.maragheh.ac.ir/article_39952.html
10.22130/scma.2020.114523.680
1
In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.
0

33
70


Reyhaneh
Bagheri
Department of Mathematics, Faculty of Science, Arak University, Arak 3815688349, Arak, Iran.
Iran
bagheri.reyhaneh@gmail.com


Davood
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University, Arak 3815688349, Arak, Iran.
Iran
alimohammadi.davood@gmail.com
Compact operator
Extended Lipschitz algebra
Lipschitz mapping
Supercontactive mapping
Weighted composition operator
[[1] H. Alihoseini and D. Alimohammadi, (1)Weak amenability of second dual of real Banach algebras, Sahand Commun. Math. Anal., 12 (2018), pp. 5988.##[2] D. Alimohammadi and S. Daneshmand, Weighted composition operators between Lipschitz algebras of complexvalued bounded functions, Caspian J. Math. Sci., 9 (2020), pp. 100123.##[3] D. Alimohammadi and S. Moradi, Some dense linear subspaces of extended little Lipschitz algebras, ISRN Mathematical Analysis, Article ID 187952, (2011), 10 pages.##[4] D. Alimohammadi and S. Moradi, Sufficient conditions for density in extended Lipschitz algebras, Caspian J. Math. Sci., 3 (2014), pp. 141151.##[5] D. Alimohammadi, S. Moradi and E. Analoei, Unital compact homomorphisms between extended Lipschitz algebras, Advances and Applications in Mathematical Sciences, 10 (2011), pp. 307330.##[6] S. Daneshmand and D. Alimohammadi, Weighted composition operators between Lipschitz spaces on pointed metric spaces, Operators and Matrices, 13 (2019), pp. 545561.##[7] A. Golbaharan and H. Mahyar, Weighted composition operators of Lipschitz algebras, Houston J. Math. 42 (2016), pp. 905917.##[8] T.G. Honary and S. Moradi, On the maximal ideal spaces of extended analytic Lipschitz algebras, Quaestiones Mathematicae, 30 (2007), pp. 349353.##[9] A. JimenezVargas and M. VillegasVallecillos, Compact composition operators on noncompact Lipschitz spaces, J. Math. Anal. Appl., 398 (2013), pp. 221229.##[10] H. Kamowitz and S. Scheinberg, Some properties of endomorphisms of Lipschitz algebras, Stud. Math., 96 (1990), pp. 255261.##[11] M. Mayghani and D. Alimohammadi, Closed ideals, point derivations and weak amenability of extended little Lipschitz algebras, Caspian J. Math. Sci., 5 (2016), pp. 2335.##[12] M. Mayghani and D. Alimohammadi, The structure of ideals, point derivations, amenability and weak amenability of extended little Lipschitz algebras, Int. J. Nonlinear Anal. Appl., 8 (2017), pp. 389404.##[13] W. Rudin, Real and Complex Analysis, McGrawHill, NewYork, Third Edition, 1987.##[14] D.R. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math., 13 (1963), 13871399.##[15] D.R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc., 111 (1964), pp. 240272.##[16] N. Weaver, Lipschitz algebras, World Scientific, Singapore, 1999.##]
1

Strong Convergence of the Iterations of Quasi $phi$nonexpansive Mappings and its Applications in Banach Spaces
https://scma.maragheh.ac.ir/article_39052.html
10.22130/scma.2019.115400.687
1
In this paper, we study the iterations of quasi $phi$nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$nonexpansive mappings. Then, we give applications of our main results in equilibrium problems.
0

71
80


Rasoul
Jahed
Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.
Iran
rjahed@iaugermi.ac.ir


Hamid
Vaezi
Department of Mathematics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran.
Iran
hvaezi@tabrizu.ac.ir


Hossein
Piri
Department of Mathematics, University of Bonab, Bonab, Iran.
Iran
h.piri@bonabu.ac.ir
Demiclosed
equilibrium problem
fixed point
hybrid projection
quasi nonexpansive mapping
Resolvent
[[1] Y.I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications. Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., 178, Dekker, New York, 1996, pp. 1550.##[2] O. Guler, On the convergence of the proximal point algorithm for convex minimization, SIAM J. Control Optim., 29 (1991), pp. 403419.##[3] A.N. Iusem and M. Nasri, Inexact proximal point methods for equilibrium problems in Banach spaces, Numer. Funct. Anal. Optim., 28 (2007), pp. 12791308.##[4] S. Kamimura and W. Takahashi, Strong convergence of a proximaltype algorithm in a Banach space, SIAM J. Optim., 13 (2002), no. 3, pp. 938945.##[5] H. Khatibzadeh and V. Mohebbi, On the iterations of a sequence of strongly quasinonexpansive mappings with applications, Numer. Funct. Anal. Optim., (2019) doi: 10.1080/01630563.2019.1626419.##[6] H. Khatibzadeh and V. Mohebbi, On the proximal point method for an infinite family of equilibrium problems in Banach spaces, Bull. Korean Math. Soc., 56 (2019), pp. 757777.##[7] F. Kohsaka and W. Takahashi, Strong convergence of an iterative sequence for maximal monotone operators in a Banach space, Abstr. Appl. Anal., (2004), pp. 239249.##[8] Z. Ma, L. Wang and S. Chang, Strong convergence theorem for quasi$phi$asymptotically nonexpansive mappings in the intermediate sense in Banach spaces, J. Inequal. Appl., (2013) 2013:306, 13 pp.##[9] B. Martinet, Regularisation d'Inequations Variationnelles par Approximations Successives, Revue Francaise d'Informatique et de Recherche Operationnelle, 3 (1970), pp. 154158.##[10] S. Reich, A weak convergence theorem for the alternating method with Bregman distances, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., 178, Dekker, New York, (1996), pp. 313318.##[11] R.T. Rockafellar, Characterization of the subdifferentials of convex functions, Pacific J. Math., 17 (1966), pp. 497510.##[12] R.T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1976), pp. 877898.##[13] R.T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pacific J. Math., 33 (1970), pp. 209216.##]
1

Uniform Convergence to a Left Invariance on Weakly Compact Subsets
https://scma.maragheh.ac.ir/article_40529.html
10.22130/scma.2019.100548.540
1
Let $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $aa_alphavarphi(a)a_alphato0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such as Segal algebras and $L^1$algebras are responsive to this concept. It is also shown that $Wap(A)$ has a left invariant $varphi$mean if and only if there exists a bounded net $left{a_alpharight}_{alphain I}$ in $left{ain A; varphi(a)=1right}$ such that $aa_alphavarphi(a)a_alpha_{Wap(A)}to0$ uniformly for all $a$ in weakly compact subsets of $A$. Other results in this direction are also obtained.
0

81
91


Ali
Ghaffari
Department of Mathematics, Faculty of Science, University of Semnan, P.O.Box 35195363, Semnan, Iran.
Iran
aghaffari@semnan.ac.ir


Samaneh
Javadi
Faculty of Engineering East Guilan, University of Guilan, P. O. Box 4489163157, Rudsar, Iran.
Iran


Ebrahim
Tamimi
Department of Mathematics, Faculty of Science, University of Semnan, P.O.Box 35195363, Semnan, Iran.
Iran
Banach algebra
$varphi$amenability
$varphi$means
Weak almost periodic
Weak$^*$ topology
[[1] A. Azimifard, $alpha$amenable hypergroups, Math. Z., 265 (2010), pp. 971982.##[2] A. Azimifard, On the $alpha$amenability of hypergroups, Monatsh Math., 115 (2008), pp. 113.##[3] H.G. Dales, Banach algebra and automatic continuity, London Math. Soc. Monogr. Ser. Clarendon Press, 2000.##[4] J. Duncan and S.A.R. Hosseiniun, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh Sect. A, 84 (1979), pp. 309325.##[5] R.E. Edwards, Functional analysis, NewYork, Holt, Rinehart and Winston, 1965.##[6] F. Filbir, R. Lasser, and R. Szwarc, Reiter's condition $P_1$ and approximate identities for hypergroups, Monatsh Math., 143 (2004), pp. 189203.##[7] G.B. Folland, A course in abstract harmonic analysis, CRC Press, Boca Raton, FL, 1995.##[8] A. Ghaffari, Strongly and weakly almost periodic linear maps on semigroup algebras, Semigroup Forum, 76 (2008), pp. 95106.##[9] Z. Hu, M.S. Monfared, and T. Traynor, On character amenable Banach algebras, Studia Math., 193 (2009), pp. 5378.##[10]B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972).##[11] E. Kaniuth, A.T. Lau, and J. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl., 344 (2008), pp. 942955.##[12] E. Kaniuth, A.T. Lau and J. Pym, On $varphi$amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144 (2008), pp. 8596.##[13] J.L. Kelley, General topology, Van Nostrand, Princeton, N. J., 1955.##[14] A.T. Lau, Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups, Fund. Math., 118 (1983), pp. 161175.##[15] M.S. Monfared, Character amenability of Banach algebras, Math. Proc. Camb. Phil. Soc., 144 (2008), pp. 697706.##[16] J.P. Pier, Amenable locally compact groups, John Wiley And Sons, New York, 1984.##[17] H. Reiter, $L^1$algebras and Segal Algebras, Lecture Notes in Mathematics, Vol. 231, SpringerVerlag, Berlin/ New York, 1971.##[18] W. Rudin, Functional analysis, McGraw Hill, New York, 1991.##]
1

On Some Characterization of Generalized Representation WavePacket Frames Based on Some Dilation Group
https://scma.maragheh.ac.ir/article_40531.html
10.22130/scma.2019.106144.592
1
In this paper we consider (extended) metaplectic representation of the semidirect product $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$ where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Finally, we rewrite the dual conditions, by using the Wigner distribution and obtain more reconstruction formulas.
0

93
106


Atefe
Razghandi
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.
Iran
ateferazghandi@yahoo.com


Ali Akbar
Arefijamaal
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.
Iran
arefijamaal@gmail.com
Representation frames
Dilation groups
Dual frames
Continuous frames
[[1] S.T. Ali, J.P. Antoine and J.P. Gazeau, Coherent states, wavelets and their generalizations, SpringerVerlag, New York, 2000.##[2] S.T. Ali, J.P. Antoine and J.P. Gazeau, Continuous frames in Hilbert spaces, Ann. Physics, 222 (1993), pp. 137.##[3] J.P. Antoine, The continuous wavelet transform in image processing, CWI Quarterly, 1 (1998), pp. 323346.##[4] A. Arefijamaal and S. Ghasemi, On characterization and stability of alternate dual of gframes, Turk. J. Math. 37 (2013), pp. 7179.##[5] P.G. Casazza, G. Kutyniok and M.C. Lammers, Duality principles in frame theory, J. Fourier Anal. Appl. 10 (2004), pp. 383408.##[6] O. Christensen, Frames and Bases: An Introductory Course, Birkhauser, Boston, 2008.##[7] O. Christensen and S.S. Goh, From dual pairs of Gabor frames to dual pairs of wavelet frames and vice versa, Appl. Comput. Harmon. Anal., 36 (2014), pp. 198214.##[8] E. Cordero, F.D. Mari, K. Nowak and A. Tabacco, Analytic features of reproducing groups for the metaplectic representation, J. Fourier Anal. appl. 12 (2006), pp. 157180.##[9] E. Cordero, E.D. Mari, K. Nowak and A. Tabacco, Dimensional upper bounds for admissible subgroups for the metaplectic representation, Math. Nachr. 283 (2010), pp. 982993.##[10] E. Cordero and A. Tabacco, Triangular Subgroups of Sp(d;R) and Reproducing Formulae, J. Funct. Anal. 264 (2013), pp. 20342058.##[11] I. Daubechies, The wavelet transform, timefrequency localization and signal analysis, IEEE Trans. Inform. Theory 36 (1990), pp. 9611005.##[12] M.N. Do and M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation, IEEE Trans. Image Process, 14 (2005), pp. 20912016.##[13] M. DuvalDestin, M.A. Muschietti and B. Torresani, Continuous wavelet decompositions, multiresolution and contrast analysis, SIAM J. Math. Anal. 24 (1993), pp. 739755.##[14] G.B. Folland, Harmonic Analysis in Phase Space, Princeton University Press, 1989.##[15] G.B. Folland, A Course in Abstract Harmonic Analysis, CRC Press: Boca Raton, 1995.##[16] M. Frazier, G. Garrigos, K. Wang and G. Weiss, A characterization of functions that generate wavelet and related expansions, J. Fourier Anal. Appl. 3 (1997), 883906.##[17] A. Ghaani Farashahi, Squareintegrability of multivariate metaplectic wavepacket representations, J. Phys. A, 50 (2017), pp. 115202.##[18] A. Ghaani Farashahi, Squareintegrability of metaplectic wavepacket representations on $L^2(mathbb{R})$}, J. Math. Anal. Appl., 449 (2017), pp. 769792.##[19] A. Ghaani Farashahi, Abstract harmonic analysis of wave packet transforms over locally compact abelian groups, Banach J. Math. Anal., 11 (2017), pp. 5071.##[20] A. Ghaani Farashahi, Multivariate wavepacket transforms, J. Anal. Appl., 36 (2017), pp. 481500.##[21] A. Ghaani Farashahi, Wave packet transforms over finite cyclic groups, Linear Algebra Appl., 489 (2016), pp. 7592.##[22] A. Ghaani Farashahi, Wave packet transform over finite fields, Electron. J. Linear Algebra, 30 (2015), pp. 507529.##[23] D. Gosson, Symplectic Geometry and Quantum Mechanics, Birkhauser, Basel, 2006.##[24] K. Grochenig, Foundations of TimeFrequency Analysis, Birkhauser, Boston, 2001.##[25] D. Han, Frame representations and parseval duals with applications to Gabor frames, Trans. Amer. Math. Soc., 360 (2008), pp. 33073326.##[26] G. Kaiser, A Firendly Guide to wavelets, Birkhauser, Boston, 1994.##[27] V.P. Maslov and M.V. Fedoriuk, SemiClassical Approximations in Quantum Mechanics, Reidel, Boston, 1981.##]
1

About SubspaceFrequently Hypercyclic Operators
https://scma.maragheh.ac.ir/article_43323.html
10.22130/scma.2020.117046.707
1
In this paper, we introduce subspacefrequently hypercyclic operators. We show that these operators are subspacehypercyclic and there are subspacehypercyclic operators that are not subspacefrequently hypercyclic. There is a criterion like to subspacehypercyclicity criterion that implies subspacefrequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is subspacefrequently hypercyclic. Additionally, operators on finite spaces can not be subspacefrequently hypercyclic.
0

107
116


Mansooreh
Moosapoor
Assistant Professor, Department of Mathematics, Farhangian University, Tehran, Iran.
Iran
mosapor110@gmail.com


Mohammad
Shahriari
Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box5518183111, Maragheh, Iran.
Iran
shahriari@maragheh.ac.ir
Subspacefrequently hypercyclic operators
Subspacehypercyclic operators
Frequently hypercyclic operators
Hypercyclic operators
[[1] N. Bamerni, V. Kadets and A. Kilicman, Hypercyclic operators are subspacehypercyclic, J. Math. Anal. Appl., 435(2)(2016), pp. 18121815.##[2] F. Bayart and S. Grivaux, Frequently hypercyclic operators, Trans. Amer. Math. Soc., 358(11) (2006), pp. 50835117.##[3] F. Bayart and S. Grivaux, Invariant Gaussian measures for operators on Banach spaces and linear dynamics, Proc. London Math. Soc., 94(3) (2007), pp. 181210.##[4] A. Bonilla and K.G. GrosseErdmann, Frequently hypercyclic operators and vectors, Ergod. Theor. Dyn. Syst., 27 (2007), pp. 383404.##[5] S. Grivaux, Frequently hypercyclic operators with irregularly visiting orbits, J. Math. Anal. Appl., 462 (2018), pp. 542553.##[6] K.G. GrosseErdmann, Frequently hypercyclic bilateral shifts, Glasgow. Math. J., 61(2) (2019), pp. 271286.##[7] K.G. GrosseErdmann and A. Peris, Frequently dense orbits, C. R. Acad. Sci. Paris, Ser. I, 341 (2005), pp. 123128.##[8] K.G. GrosseErdmann and A. Peris Manguillot, Linear chaos, Springer, 2011.##[9] B.F. Madore and R.A. MartinezAvendano, Subspace hypercyclicity, J. Math. Anal. Appl., 373(2) (2011), pp. 502511.##[10] R.A. MartinezAvendano and O. ZatarainVera, Subspacehypercyclicity for Toeplitz operators, J. Math. Anal. Appl., 422(1) (2015), pp. 772775.##[11] Q. Menet, Linear chaos and frequent hypercyclicity, Trans. Amer. Math. Soc., 369(7) (2017), pp. 49774994.##[12] H. Rezaei, Notes on subspacehypercyclic operators, J. Math. Anal. Appl., 397(1) (2013), pp. 428433.##[13] S. Shkarin, On the spectrum of frequently hypercyclic operators, Proc. Amer. Math. Soc., 137(1) (2009), pp. 123134.##[14] T.K. Subrahmonian Moothathu, Two remarks on frequent hypercyclicity, J. Math. Anal. Appl., 408 (2013), pp. 843845.##[15] S. Talebi and M. Moosapoor, Subspacechaotic operators and subspaceweakly mixing operators, Int. J. of Pure and Applied Math., 78 (2012), pp. 879885.##]
1

On the Spaces of $lambda _{r}$almost Convergent and $lambda _{r}$almost Bounded Sequences
https://scma.maragheh.ac.ir/article_40579.html
10.22130/scma.2019.111716.644
1
The aim of the present work is to introduce the concept of $lambda _{r}$almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$almost convergent and $lambda _{r}$almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $ and $gamma $duals of the space $fleft( lambda _{r}right) $. Finally, we give the characterization of some matrix classes.
0

117
130


Sinan
Ercan
Department of Mathematics, Faculty of Science, Firat University, 23119, Elazig, Turkey.
Turkey
sinanercan45@gmail.com
Almost convergence
Matrix domain
$beta $
$gamma $duals
Matrix transformations
[[1] A. Sonmez, Almost convergence and triple band matrix, Math. Comput. Modelling, 57 (2013), pp. 23932402.##[2] M. Candan, Almost convergence and double sequential band matrix, Acta. Math. Sci., 34 (2014), pp. 354366.##[3] M. Kirisci, Almost convergence and generalized weighted mean II, J. Inequal. Appl., 1 (2014), pp. 113.##[4] M. Kirisci, Almost convergence and generalized weighted mean, In: AIP Conference Proceedings, AIP (2012), pp. 191194.##[5] M. Sengonul and K. Kayaduman, On the Riesz almost convergent sequences space, Abstr. Appl. Anal., 2012 (2012), Article ID 691694, 18 pages.##[6] A. Karaisa and F. Ozger, Almost difference sequence space derived by using a generalized weighted mean, J. Comput. Anal. Appl., 19 (2015), pp. 2738.##[7] F. Basar and R. Colak, Almostconservative matrix transformations, Turkish J. Math., 13 (1989), pp. 91100.##[8] M. Kirisci, On the spaces of Euler almost null and Euler almost convergent sequences, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 62 (2013), pp. 116.##[9] Qamaruddin, S.A. Mohuiddine, Almost convergence and some matrix transformations, Filomat, 21 (2007), pp. 261266.##[10] M. Candan and K. Kayaduman, Almost convergent sequence space derived by generalized Fibonacci matrix and Fibonacci core, Brithish J. Math. Comput. Sci., 7 (2015), pp. 150167.##[11] F. Basar and M. Kirisci, Almost convergence and generalized difference matrix, Comput. Math. Appl., 61 (2011), pp. 602611.##[12] M. Mursaleen and A. K. Noman, On the spaces of $lambda$convergent sequences and bounded sequences, Thai J. Math, 8 (2010), pp. 311329.##[13] P.N. Ng and P.Y. Lee, Cesaro sequence spaces of nonabsolute type, Comment. Math. Prace Mat., 20 (1978), pp. 429433.##[14] M. Sengonul and F. Basar, Some new Cesaro sequence spaces of nonabsolute type which include the spaces $c_0$ and $c$, Soochow J. Math., 31 (2005), pp. 107119.##[15] M. Yesilkayagil and F. Basar, Space of $A_lambda $almost null and $A_lambda $almost convergent sequences, J. Egypt. Math. Soc., 23 (2015), pp. 119126.##[16] A. Wilansky, Summability Through Functional Analysis, in: NorthHolland Mathematics Studies, Elsevier Science Publishers, Amsterdam, New York, 1984.##[17] G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80 (1948), pp. 167190.##[18] A. M. Jarrah and E. Malkowsky, BK spaces, bases and linear operators, Ren. Circ. Mat. Palermo II, 52 (1990), pp. 177191.##[19] H.I. Miller and C. Orhan, On almost convergent and statistically convergent subsequences, Acta Math. Hungar., 93 (2001), pp. 135151.##[20] G.M. Petersen, Regular Matrix Transformations, McGrawHill, New YorkTorontoSydney, 1970.##[21] J.A. Siddiqi, Infinite matrices summing every almost periodic sequences, Pac. J. Math., 39 (1971), pp. 235251.##[22] J.P. Duran, Infinite matrices and almost convergence, Math. Z., 128 (1972), pp. 7583.##[23] J.P. King, Almost summable sequences, Proc. Am. Math. Soc., 17 (1966), pp. 12191225.##[24] F. Basar and I. Solak, Almostcoercive matrix transformations, Rend. Mat. Appl., 11 (1991), pp. 249256.##[25] F. Basar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul, 2012.##[26] S. Nanda, Infinite matrices and almost convergence, J. Indian Math. Soc., 40 (1976), pp. 173184.##[27] P. Korus, On $Lambda ^r$strong convergence of numerical sequences and Fourier series, J. Class. Anal., 9 (2016), pp. 8998.##[28] S. Ercan, On $lambda_r$Convergence and $lambda_r$Boundedness, Journal of Advanced Physics, 7 (2018), pp. 123129.##]
1

Almost MultiCubic Mappings and a Fixed Point Application
https://scma.maragheh.ac.ir/article_40581.html
10.22130/scma.2019.113393.665
1
The aim of this paper is to introduce $n$variables mappings which are cubic in each variable and to apply a fixed point theorem for the HyersUlam stability of such mapping in nonArchimedean normed spaces. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes are presented.
0

131
143


Nasrin
Ebrahimi Hoseinzadeh
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Iran
nasrin_ebrahimi_h@yahoo.com


Abasalt
Bodaghi
Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran.
Iran
abasalt.bodaghi@gmail.com


Mohammad Reza
Mardanbeigi
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
Iran
mrmardanbeigi@srbiau.ac.ir
Multicubic mapping
HyersUlam stability
Fixed point
nonArchimedean normed space
[[1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan., 2 (1950), pp. 6466.##[2] A. Bahyrycz, K. Cieplinski and J. Olko, On HyersUlam stability of two functional equations in nonArchimedean spaces, J. Fixed Point Theory Appl., 18 (2016), pp. 433444.##[3] A. Bodaghi, Ulam stability of a cubic functional equation in various spaces, Mathematica, 55(2) (2013), pp. 125141.##[4] A. Bodaghi, Cubic derivations on Banach algebras, Acta Math. Vietnam., 38(4) (2013) , pp. 517528.##[5] A. Bodaghi, Intuitionistic fuzzy stability of the generalized forms of cubic and quartic functional equations, J. Intel. Fuzzy Syst., 30 (2016), pp. 23092317.##[6] A. Bodaghi, I.A. Alias and M.H. Ghahramani, Approximately cubic functional equations and cubic multipliers, J. Inequal. Appl., 53 (2011):53, doi:10.1186/1029242X201153.##[7] A. Bodaghi, S.M. Moosavi and H. Rahimi, The generalized cubic functional equation and the stability of cubic Jordan $*$derivations, Ann. Univ. Ferrara, 59 (2013), pp. 235250.##[8] A. Bodaghi, C. Park and O.T. Mewomo, Multiquartic functional equations, Adv. Difference Equ., 2019, 2019:312, https://doi.org/10.1186/s1366201922555##[9] A. Bodaghi and B. Shojaee, On an equation characterizing multicubic mappings and its stability and hyperstability, Fixed Point Theory, to appear, arXiv:1907.09378v2##[10] J. Brzdek and K. Cieplinski, A fixed point approach to the stability of functional equations in nonArchimedean metric spaces, Nonlinear Anal., 74 (2011), pp. 68616867.##[11] J. Brzdek and K. Cieplinski, Hyperstability and Superstability, Abstr. Appl. Anal., 2013, Art. ID 401756, 13 pp.##[12] K. Cieplinski, Generalized stability of multiadditive mappings, Appl. Math. Lett., 23 (2010), pp. 12911294.##[13] K. Cieplinski, On the generalized HyersUlam stability of multiquadratic mappings, Comput. Math. Appl., 62 (2011), pp. 34183426.##[14] P. Gavruta, A generalization of the HyersUlamRassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), pp. 431436.##[15] K. Hensel, Uber eine neue Begrndung der Theorie der algebraischen Zahlen, Jahresber, Deutsche MathematikerVereinigung, 6 (1897), pp. 8388.##[16] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., U.S.A., 27 (1941), pp. 222224.##[17] K.W. Jun and H.M. Kim, The generalized HyersUlamRussias stability of a cubic functional equation, J. Math. Anal. Appl., 274 (2002), no. 2, 267278.##[18] K.W. Jun and H.M. Kim, On the HyersUlamRassias stability of a general cubic functional equation, Math. Inequ. Appl., 6(2) (2003), pp. 289302.##[19] A. Khrennikov, NonArchimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Mathematics and its Applications, Vol. 427, Kluwer Academic Publishers, Dordrecht, 1997.##[20] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality, Birkhauser Verlag, Basel, 2009.##[21] C. Park and A. Bodaghi, Two multicubic functional equations and some results on the stability in modular spaces, J. Inequal. Appl., 2020, 6 (2020).##[22] J.M. Rassias, Solution of the Ulam stability problem for cubic mappings, Glasnik Matematicki. Serija III., 36(1) (2001), pp. 6372.##[23] J.M. Rassias, On approximately of approximately linear mappings by linear mappings, J. Funct. Anal., 46 (1982), pp. 126130.##[24] Th.M. Rassias, On the stability of the linear mapping in Banach Space, Proc. Amer. Math. Soc., 72(2) (1978), pp. 297300.##[25] S. Salimi and A. Bodaghi, A fixed point application for the stability and hyperstability of multiJensenquadratic mappings, J. Fixed Point Theory Appl., (2020) 22:9, https://doi.org/10.1007/s1178401907383.##[26] S.M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.##[27] T.Z. Xu, Stability of multiJensen mappings in nonArchimedean normed spaces, J. Math. Phys., 53, 023507 (2012); doi: 10.1063/1.368474.##[28] T.Z. Xu, Ch. Wang and Th.M. Rassias, On the stability of multiadditive mappings in nonArchimedean normed spaces, J. Comput. Anal. Appl., 18 (2015), pp. 11021110.##[29] S.Y. Yang, A. Bodaghi and K.A.M. Atan, Approximate cubic $*$derivations on Banach $*$algebras, Abstr. Appl. Anal., 2012, Art. ID 684179, 12 pp.##[30] X. Zhao, X. Yang and C.T. Pang, Solution and stability of the multiquadratic functional equation, Abstr. Appl. Anal., 2013, Art. ID 415053, 8 pp.##]
1

Continuous $ k $Frames and their Dual in Hilbert Spaces
https://scma.maragheh.ac.ir/article_40583.html
10.22130/scma.2019.115719.691
1
The notion of $k$frames was recently introduced by Gu avruc ta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$frame, so called c$k$frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a c$k$frame and prove some new results about it.
0

145
160


Gholamreza
Rahimlou
Department of Mathematics, Shabestar Branch,Islamic Azad University, Shabestar, Iran.
Iran
grahimlou@gmail.com


Reza
Ahmadi
Institute of Fundamental Science, University of Tabriz, Tabriz, Iran.
Iran
rahmadi@tabrizu.ac.ir


Mohammad Ali
Jafarizadeh
Faculty of Physic, University of Tabriz, Tabriz, Iran.
Iran
jafarizadeh@tabrizu.ac.ir


Susan
Nami
Faculty of Physic, University of Tabriz, Tabriz, Iran.
Iran
s.nami@tabrizu.ac.ir
cframe
$K$frame
c$K$frame
c$k$atom
c$k$dual
[[1] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Continuous frames in Hilbert spaces, Ann.Phys., 222 (1993), pp. 137.##[2] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Coherent States, Wavelets and their Generalizations, Springer Graduate Texts in Contemporary Physics, 1999.##[3] F. Arabyani and A.A. Arefijamal, Some constructions of $k$frames and their duals, Rocky Mountain., 47(6)(2017), pp. 17491764.##[4] J. Benedetto, A. Powell, and O. Yilmaz, SigmaDelta quantization and finite frames, IEEE Trans. Inform.Th., 52(2006), pp. 19902005.##[5] H. Bolcskel , F. Hlawatsch, and H.G Feichyinger, FrameTheoretic analysis of oversampled filter bank, IEEE Trans. Signal Processing.,46(12)(1998), pp. 3256 3268.##[6] E.J. Candes and D.L. Donoho, New tight frames of curvelets and optimal representation of objects with piecwise $C^2$ singularities, Comm. Pure and App. Math.,56 (2004), pp. 216266.##[7] P.G. Casazza and G. Kutyniok, Frame of subspaces, Contemp. Math. 345, Amer. Math. Soc., Providence, RI., (2004), pp. 87113.##[8] P.G. Casazza, G. Kutyniok, and S. Li, Fusion frames and Distributed Processing, Appl. Comput. Harmon. Anal.,25 (2008), pp. 114132.##[9] P.G. Casazza and J. Kovacevic, Equalnorm tight frames with erasures, Adv. Comput. Math., 18 (2003), pp. 387430.##[10] O. Christensen, An Introduction to Frames and Riesz Bases, 2nd ed. Birkhauser,Boston, 2016.##[11] I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal Expansions, J. Math. Phys., 27(1986), pp. 12711283.##[12] R.G. Douglas, On majorization, factorization and range inclusion of operators on Hilbert spaces, Proc. Amer. Math. Soc., 17(2) (1966), pp. 413415.##[13] R.J. Duffin and A.C. Schaeffer, A class of nonharmonik Fourier series, Trans. Amer. Math. Soc.,72 (1952), pp. 341366.##[14] M.H. Faroughi and E. Osgooei, CFrames and CBessel Mappings, Bull. Iranian Math. Soc., 38(1) (2012), pp. 203222.##[15] M. Fornasier and H. Rauhut, Continuous frames, function spaces, and the discretization problem, J. Fourier Anal. Appl., 11(3) (2005), pp.245287.##[16] J.P. Gabardo and D. Han, Frames associated with measurable spaces, Adv. Comput. Math., 18(2003), pp.127147.##[17] L.Gavruta, Frames for operators, Appl. Comput. Harmon. Anal.,32 (2012), pp. 139144.##[18] B. Hassibi, B. Hochwald, A. Shokrollahi, and W. Sweldens, Representation theory for highrate multipleantenna code design, IEEE Trans. Inform.Theory., 47 (2001), pp. 23352367.##[19] G. Kaiser, A Friendly Guide to Wavelets, Birkhuser Boston, 2011.##[20] M. Mirzaee, M. Rezaei, and M.A. Jafarizadeh, Quantum tomography with wavelet transform in Banach space on homogeneous space, Eur. Phys. J. B., 60 (2007), pp. 193201.##[21] A. Rahimi A. Najati, and Y.N. Dehgan, Continuous frame in Hilbert space, Methods Func. Anal. Top., 12 (2006), pp. 170182.##[22] A. Rahimi, A. Najati, and M H. Faroughi, Continuous and discrete frames of subspaces in Hilbert spaces, Southeast Asian Bull. Math., 32 (2008), pp. 305324.##[23] M. Rahmani, On some properties of cframes, J. Math. Research with Appl., 37(4) (2017), pp. 466476.##[24] W. Rudin, Functional Analysis, New York, Tata Mc GrawHill Editions, 1973.##[25] W. Rudin, Real and Complex Analysis, New York, Tata Mc GrawHill Editions, 1987.##[26] S. Sakai, $C^*$Algebras and $W^*$Algebras, New York, SpringerVerlag, 1998.##[27] X. Xiao, Y. Zhu, and L. Gavruta, Some Properties of $k$frames in Hilbert Spaces, Results. Math., 63 (2012), pp.12431255.##]
1

$n$factorization Property of Bilinear Mappings
https://scma.maragheh.ac.ir/article_40584.html
10.22130/scma.2019.116000.696
1
In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$factorization property of level $kappa$. Then we study the relation between $n$factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$$w^*$continuity and also strong Arens irregularity. These results may help us to prove some previous problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~cite{neu1} and ~cite{neu}. Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to the GhahramaniLau conjecture is raised.
0

161
173


Sedigheh
Barootkoob
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
Iran
s.barutkub@ub.ac.ir
Bilinear map
Factorization property
Strongly Arens irregular
Automatically bounded and $w^*$$w^*$continuous
[[1] G.R. Allan and A.M. Sinclair, Bounded approximate identities, factorization, and a convolution algebra, J. Funct. Anal., 29 (1978), pp. 308318.##[2] G.R. Allan and A.M. Sinclair, Power factorization in Banach algebras with bounded approximate identity, Studia Math., 56 (1976), pp. 3138.##[3] A. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc., 2 (1951), pp. 839848.##[4] S. Barootkoob, Topological centers and factorization of certain module actions, Sahand Commun. Math. Anal., 15 (1) (2019), pp. 203215.##[5] P. Cohen, Factorization in group algebras, Dllke Math. J., 26 (1959), pp. 199205.##[6] H.G. Dales, Banach algebras and automatic continuity, Vol. 24 of London Mathematical Society Monographs, The Clarendon Press, Oxford, UK, 2000.##[7] F. Ghahramani and A.T.M. Lau, Multipliers and ideals in second conjugate algebras related to locally compact groups, J. Funct. Anal., 132 (1) (1995), pp. 170191.##[8] F. Ghahramani and J.P. McClure, Module homomorphisms of the dual modules of convolution Banach algebras, Canad. Math. Bull., 35 (2) (1992), pp. 180185.##[9] M. Eshaghi Gordji and M. Filali, Arens regularity of module actions, Studia Math., 181 (3) (2007), pp. 237254.##[10] N. Gronbaek, Power factorization in Banach modules over commutative radical Banach algebras, Math. Scand., 50 (1982), pp. 123134.##[11] K. Haghnejad Azar, Arens Regularity and Factorization Property, J. Sci. Kharazmi University, 13 (2) (2013), pp. 321336.##[12] K. Haghnejad Azar, Factorization properties and generalization of multipliers in module actions, Journal of Hyperstructures, 4 (2) (2015), pp. 142155.##[13] K. Haghnejad Azar and Masoud Ghanji, Factorization properties and topologicalL centers of module actions and $*$involution algebras, U.P.B. Sci. Bull., Series A, 75 (1) (2013), pp. 3546.##[14] E. Hewitt and K. A. Ross, Abstract harmonic analysts, Volume II: Structure and analysts for compact groups, analysis on locally compart Abeltan gnmps, SpringerVerlag, Berlin, Heidelberg, and New York, 1970.##[15] H. Hofmeier and G. Wittstock, A bicommutant theorem for completely bounded module homomorphisms, Math. Ann., 308 (1) (1997), pp. 141154.##[16] Z. Hu and M. Neufang, Decomposability of von Neumann algebras and the Mazur property of higher level, Canad. J. Math., 58 (4) (2006), pp. 768795.##[17] B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972).##[18] A. T.M Lau and A. Ulger, Topological centers of certain dual algebras, Trans. Amer. Math. Soc., 348 (3) (1996), pp. 11911212.##[19] V. Losert, M. Neufang, J. Pachl, and J. Steprans, Proof of the Ghahramani–Lau conjecture, Advanc. Math., 290 (2016), pp. 709738.##[20] M. Neufang, On a conjecture by GhahramaniLau and related problems concerning topological centers, J. Funct. Anal., 224 (1) (2005), pp. 217229.##[21] M. Neufang, On Mazur's property and property (X), J. Operat. Theory, 60 (2) (2008), pp. 301316.##[22] M. Neufang, Solution to a conjecture by HofmeierWittstock, J. Funct. Anal., 217 (1) (2004), pp. 171180.##[23] D. Poulin, Characterization of amenability by a factorization property of the group Von Neumann algebra, arXiv:1108.3020v1 [math.OA] (2011).##]
1

Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra
https://scma.maragheh.ac.ir/article_37420.html
10.22130/scma.2018.77951.362
1
In this paper, we discuss some properties of joint spectral {radius(jsr)} and generalized spectral radius(gsr) for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*left(Sigmaright)= hat{r}left(Sigmaright)$, but for a bounded set of upper triangular matrices with entries in a Banach algebra($Sigma$), $r_*left(Sigmaright)neqhat{r}left(Sigmaright)$. We investigate when the set is defective or not and equivalent properties for having a norm equal to jsr, too.
0

175
188


Hamideh
Mohammadzadehkan
Department of Mathematics, Faculty of Science, Payame Noor University, P.O.Box 193953697, Tehran, Iran.
Iran
mohammadzadeh83@gmail.com


Ali
Ebadian
Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.
Iran
ebadian.ali@gmail.com


Kazem
Haghnejad Azar
Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran.
Iran
haghnejad@uma.ac.ir
Banach algebra
Upper Triangular Matrix
Generalized Spectral Radius
Joint Spectral Radius
Geometric Joint Spectral Radius
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1

On Fixed Point Results for Hemicontractivetype Multivalued Mapping, Finite Families of Split Equilibrium and Variational Inequality Problems
https://scma.maragheh.ac.ir/article_39955.html
10.22130/scma.2019.99206.533
1
In this article, we introduced an iterative scheme for finding a common element of the set of fixed points of a multivalued hemicontractivetype mapping, the set of common solutions of a finite family of split equilibrium problems and the set of common solutions of a finite family of variational inequality problems in real Hilbert spaces. Moreover, the sequence generated by the proposed algorithm is proved to be strongly convergent to a common solution of these three problems under mild conditions on parameters. Our results improve and generalize many wellknown recent results existing in the literature in this field of research.
0

189
217


Tesfalem Hadush
Meche
Department of Mathematics, College of Natural and Computational Sciences, Aksum University, P.O.Box 1020, Aksum, Ethiopia.
Ethiopia
tesfalemh78@gmail.com


Habtu
Zegeye
Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana.
Botswana
habtuzh@yahoo.com
Fixed point
multivalued, hemicontractivetype, variational inequality, split equilibrium problems
strong convergence
Monotone mapping
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