Journal of Linear and Topological Algebra: 1 (1)

Open Access Article

1 - Coupled fixed point results for $T$-contractions on $\mathcal{F}$-metric spaces and an application
H. Majani R. Zaer Soleimani Javad Izadi

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 More

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. Manuscript profile

Open Access Article

2 - Conjectures on the anti-automorphism of Z-basis of the Steenrod algebra
T. Vergili I. Karaca

20.1001.1.22520201.2021.10.01.2.6

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.

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. Manuscript profile

Open Access Article

3 - A new implicit iteration process for approximating common fixed points of $\alpha$-demicontraction semigroup
A. E. Ofem D. I. Igbokwe

20.1001.1.22520201.2021.10.01.3.7

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 ite More

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. Manuscript profile

Open Access Article

4 - Topics on a class of pseudo-Michael algebras
A. Naziri-Kordkandi

20.1001.1.22520201.2021.10.01.4.8

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 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. Manuscript profile

Open Access Article

5 - Characterization of matrices using m-projectors and singular value decomposition in Minkowski space
M. S. Lone T. H. Khan

20.1001.1.22520201.2021.10.01.5.9

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 rang More

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. Manuscript profile

Open Access Article

6 - On computing of integer positive powers for one type of tridiagonal and antitridiagonal matrices of even order
M. Beiranvand M. Ghasemi Kamalvand

20.1001.1.22520201.2021.10.01.6.0

In this paper, firstly we derive a general expression for the $m$th power ($m\in\mathbb{N}$) 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 ma More

In this paper, firstly we derive a general expression for the $m$th power ($m\in\mathbb{N}$) 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 Manuscript profile

Open Access Article

7 - Domination number of complements of functigraphs
A. Shaminejad E. Vatandoost

20.1001.1.22520201.2021.10.01.7.1

Let $G=(V, E)$ be a simple graph. A subset $S \subseteq V(G)$ is a \textit{dominating set} of $G$ if every vertex in $V(G) \setminus S$ is adjacent to at least one vertex in $S.$ The \textit{domination number} of graph $G,$ denoted by $\gamma(G),$ is the minimum size of More

Let $G=(V, E)$ be a simple graph. A subset $S \subseteq V(G)$ is a \textit{dominating set} of $G$ if every vertex in $V(G) \setminus S$ is adjacent to at least one vertex in $S.$ The \textit{domination number} of graph $G,$ denoted by $\gamma(G),$ is the minimum size of a dominating set of vertices $V(G).$ Let $G_1$ and $G_2$ be two disjoint copies of graph $G$ and $f:V(G_1)\rightarrow V(G_2)$ be a function. Then a \textit{functigraph} $G$ with function $f$ is denoted by $C(G, f),$ its vertices and edges are $V(C(G, f))=V(G_1) \cup V(G_2)$ and $E(C(G, f))=E(G_1) \cup E(G_2) \cup \{vu| v \in V(G_1) , u \in V(G_2), f(v)=u\},$ respectively. In this paper, we investigate domination number of complements of functigraphs. We show that for any connected graph $G,$ $\gamma(\overline{C(G, f)}) \leq 3.$ Also we provide conditions for the function $f$ in some graphs such that $\gamma(\overline{C(G, f)})=3.$ Finally, we prove if $G$ is a bipartite graph or a connected $k-$ regular graph of order $n \geq 4$ for $k \in \{2, 3, 4 \}$ and $G \notin \{K_{3}, K_{4}, K_{5}, H_{1}, H_{2}\},$ then $\gamma(\overline{C(G, f)}) = 2.$ Manuscript profile

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