Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080220190601Operator frame for $End_{mathcal{A}}^{ast}(mathcal{H})$8595664913ENM. RossafiDepartment of Mathematics, University of Ibn Tofail, B.P. 133, Kenitra, Morocco0000-0002-5662-6921S. KabbajDepartment of Mathematics, University of Ibn Tofail, B.P. 133, Kenitra, MoroccoJournal Article20180407Frames generalize orthonormal bases and allow representation of all the elements of the space. Frames play significant role in signal and image processing, which leads to many applications in informatics, engineering, medicine, and probability. In this paper, we introduce the concepts of operator frame for the space $End_{mathcal{A}}^{ast}(mathcal{H})$ of all adjointable operators on a Hilbert $mathcal{A}$-module $mathcal{H}$ and establish some results.http://jlta.iauctb.ac.ir/article_664913_4d9afa233e6bf23c060563459d27638a.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080220190601Generalized hyperstability of the cubic functional equation in ultrametric spaces97104664914ENY. AribouDepartment of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, MoroccoH. DimouDepartment of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, MoroccoS. KabbajDepartment of Mathematics, Faculty of Sciences, University of Ibn Tofail, BP 133 Kenitra, MoroccoJournal Article20180425In this paper, we present the generalized hyperstability results of cubic functional equation in ultrametric Banach spaces using the fixed point method.http://jlta.iauctb.ac.ir/article_664914_46da366df2af8877b7e4b74947a145ff.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080220190601Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$105115664915ENA. TahaDepartment of Mathematics and Computer Science, Beirut Arab University, PO. Box 11-5020, Beirut, LebanonM. N. AbdulrahimDepartment of Mathematics and Computer Science, Beirut Arab University, PO. Box 11-5020, Beirut, LebanonJournal Article20180609We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$. We specialize the indeterminates used in defining these representations to non zero complex numbers. We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$. We then determine necessary and sufficient conditions that guarantee the irreducibility of the tensor products of the representations of $B_3$. As for the tensor products of the representations of $B_4$, we only find sufficient conditions for the irreducibility of the tensor product.<br /> http://jlta.iauctb.ac.ir/article_664915_125c0ce47b179bffe261276a881d37f7.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080220190601An accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations117126664921ENA. M. E. BayoumiDepartment of Mathematics, Faculty of Education, Ain Shams University, Cairo, EgyptM. A. RamadanDepartment of Mathematics, Faculty of Science, Menoufia University, Shebeen El- Koom, EgyptM. Nili AhmadabadiDepartment of Mathematics, Najafabad Branch, Islamic Azad University, Najafabad, IranJournal Article20180706In this paper, an accelerated gradient based iterative algorithm for solving systems of coupled generalized Sylvester-transpose matrix equations is proposed. The convergence analysis of the algorithm is investigated. We show that the proposed algorithm converges to the exact solution for any initial value under certain assumptions. Finally, some numerical examples are given to demonstrate the behavior of the proposed method and to support the theoretical results of this paper.http://jlta.iauctb.ac.ir/article_664921_e38ec2bc4c0ca92739b961cd491d889c.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080220190601Some topological properties of fuzzy strong b-metric spaces127131664922ENT. OnerDepartment of Mathematics, Faculty of Science, Mugla Sıtkı Kocman University Mugla 48000, TurkeyJournal Article20180828In this study, we investigate topological properties of fuzzy strong b-metric spaces defined in [13]. Firstly, we prove Baire's theorem for these spaces. Then we define the product of two fuzzy strong b-metric spaces defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are complete fuzzy strong b-metric spaces. Finally it is proven that a subspace of a separable fuzzy strong b-metric space is separable.http://jlta.iauctb.ac.ir/article_664922_5f1c6163ec1ce05220835bc3b8abc6e8.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080220190601On the duality of quadratic minimization problems using pseudo inverses133143665181END. PappasDepartment of Statistics, Athens University of Economics and Business, 76 Patission Str 10434, Athens, Greece0000-0001-9415-1392G. DomazakisDepartment of Mathematics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Iroon Polytexneiou 9, 15780 Zografou, Athens, GreeceJournal Article20180902In this paper we consider the minimization of a positive semidefinite quadratic form, having a singular corresponding matrix $H$. We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method. Given this approach and based on the strong duality principle, we provide a closed formula for the calculation of the Lagrange multipliers $\lambda$ in the cases when (i) the constraint equation is consistent and (ii) the constraint equation is inconsistent, using the general normal equation. In both cases the Moore-Penrose inverse will be used to determine a unique solution of the problems. In addition, in the case of a consistent constraint equation, we also give sufficient conditions for our solution to exist using the well known KKT conditions.http://jlta.iauctb.ac.ir/article_665181_6cbe7a9128b86e3f4cca4160c123b0ce.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080220190601Best proximity point theorems in 1/2−modular metric spaces145158665694ENH. HosseiniDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranM. Eshaghi GordjiDepartment of Mathematics, Semnan University, P. O. Box 35195-363, Semnan,
IranJournal Article20181019In this paper, first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points. Finally, as consequences of these theorems, we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. We present an example to illustrate the usability of these theorems.<br /> http://jlta.iauctb.ac.ir/article_665694_a32ce418ba117cf409365b9816766ffe.pdf