Journal of Linear and Topological Algebra
Volume:8 Issue: 2, Spring 2019

‎Frames 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.

‎In this paper‎, ‎we present the‎ generalized hyperstability results of cubic functional equation in‎ ‎ultrametric Banach spaces using the fixed point method‎.

‎We 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.

‎In 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.

‎In 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.

‎In 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.

‎In 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.