Journal of Linear and Topological Algebra
Volume:10 Issue: 1, Winter 2021

The main purpose of this article is to introduce the concept of $T$-contraction type mappings in the function weighed metric spaces and to obtain some coupled fixed points theorems in this framework. Also, an example and an application of the existence of a solution of a system of nonlinear integral equations are considered to protect the main results.

In this paper, we compute the images  of some of the $Z$-basis elements under the anti-automorphism map $chi$ of the mod 2 Steenrod algebra $mathcal{A}_2$ and propose some conjectures based on our computations.

It is our purpose in this paper to introduce the concept of $alpha$-demicontractive semigroup. Also, we construct a new implicit iterative scheme for approximating the common fixed points of $alpha$-demicontractive semigroup. We prove strong convergence of our new iterative scheme to the common fixed points of $alpha$-demicontractive semigroup in Banach spaces. Our result is an improvement and generalization of several well known results in the existing literature.

In this paper, we first generalize the Gelfand-Mazur theorem for pseudo-Michael $Q$-algebras. Then some applications of the spectral mapping theorem are also investigated in $k$-Banach algebras.

In this paper we characterize different classes of matrices in Minkowski space $mathcal{M}$ by generalizing the singular value decomposition in terms of emph{m}-projectors. Furthermore, we establish results on the relation between the range spaces and rank of the range disjoint matrices by utilizing the singular value decomposition obtained in terms of emph{m}-projectors. Since there is no result on the formulation of Minkowski inverse of the sum of two matrices, we have established an expression for the Minkowski inverse of the sum of a range disjoint matrix with its Minkowski adjoint, which will ease to formulate an expression for the Minkowski inverse of the sum of two matrices in general case.

In this paper, firstly we derive a general expression for the $m$th power ($minmathbb{N}$)  for one type of tridiagonal matrices of even order.  Secondly we present a method  for computing integer powers of the  antitridiagonal  matrices that is corresponding with these matrices. Then, we present some examples to illustrate our results and  give Maple 18 procedure in order to verify our calculations

Let G=(V,E) be a simple graph. A subset S⊆V(G) is a \textit{dominating set} of G if every vertex in V(G)∖S is adjacent to at least one vertex in S. The \textit{domination number} of graph G, denoted by γ(G), is the minimum size of a dominating set of vertices V(G). Let G1 and G2 be two disjoint copies of graph G and f:V(G1)→V(G2) be a function. Then a \textit{functigraph} G with function f is denoted by C(G,f), its vertices and edges are V(C(G,f))=V(G1)∪V(G2) and E(C(G,f))=E(G1)∪E(G2)∪{vu|v∈V(G1),u∈V(G2),f(v)=u}, respectively. In this paper, we investigate domination number of complements of functigraphs. We show that for any connected graph G, γ(C(G,f)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯)≤3. Also we provide conditions for the function f in some graphs such that γ(C(G,f)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯)=3. Finally, we prove if G is a bipartite graph or a connected k− regular graph of order n≥4 for k∈{2,3,4} and G∉{K3,K4,K5,H1,H2}, then γ(C(G,f)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯)=2