Journal of Linear and Topological Algebra
Volume:10 Issue: 4, Autumn 2021

Concept of a family of local atoms in $n$-Hilbert space is being studied. $K$-frame in tensor product of $n$-Hilbert spaces is described and a characterization is given. Atomic system in tensor product of $n$-Hilbert spaces is presented and established a relationship between atomic systems in $n$-Hilbert spaces and their tensor products.

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A double cyclic code (or emph{DC code}) of length $n=k+l$ over $mathbb{Z}_2$ is a binary linear code, where any cyclic shift of the first $k$ coordinates and the last $l$ coordinates of a codeword is also a codeword. In this paper, we study the relationship between separability and self-duality of these codes. Also, we obtain the shadow code by determining the generator polynomials of the doubly even subcode of the self-dual code.
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‎In this paper, the inverse eigenvalue problem for the bordered diagonal matrices are reconsidered whose elements are equal to zero except for the first row, the first column and the diagonal elements. The necessary and sufficient conditions for existence of a symmetric bordered diagonal matrix from special spectral data have been determined. A new algorithm to make such matrices is derived and some numerical examples are given to illustrate the efficiency of the method.

In this paper, we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph. Then we support our main theorem by a non-trivial example and give some consequences of it for usual graphs.

In this article, by using the Lie symmetry method, we find the Lie symmetry group of the thin film equation. Also, the one-dimensional optimal system of Lie subalgebras is obtained. Then, we calculate the similarity reductions of the thin film equation and classify them by using the optimal system.

Here we show that the UI-iteration scheme (Udofia and Igbokwe, [24]) can be used to approximate the fixed points of contraction and nonexpansive mappings. we prove a strong and weak convergence of the iteration scheme to the fixed point of contraction and nonexpansive mappings. We also prove that the scheme is Γ-stable and data dependent. Analytically and with numerical example we show that the UI-iteration scheme has a faster rate of convergence for contraction and nonexpansive mappings than some well known existing iteration schemes in literature. Finally, we apply the UI-iteration scheme to find the solution of constrained convex minimization problem.

contractive mapping for two maps in the framework of w-distance is introduced and some fixed point results are established, which extend recent results of Lakzian and Rhoades [5] and many existing results in the literature‎. ‎In addition‎, ‎to validate the novelty of our findings‎, ‎we give an illustrative example‎, ‎which yields the main result‎. ‎Moreover‎, ‎as an application‎, ‎we employ the achieved result to earn the existence criteria of the‎ ‎solution of a type of non-linear Fredholm integral equation‎.