Journal of Linear and Topological Algebra
Volume:11 Issue: 3, Summer 2022

In this work we review some common fixed point theorems for four mappings without appealing to continuity in $\mathcal{E}$-metric spaces, where the metric is Riesz space valued. These results cover well-known comparable results in the existing literature by considering fewer conditions.

‎We obtain some new Jensen-Mercer type inequalities for log-convex functions‎. ‎Indeed‎, ‎we establish refinement and reverse for the Jensen-Mercer inequality for log-convex functions‎. ‎Several new Hermite-Hadamard and Fej\'er types of inequalities are also presented‎.‎

‎In this paper‎, ‎we prove some results on complex partial b-metric space $(\Re‎, ‎p_{b}^{c})$‎, ‎which are more generalization of S-contractive mappings‎. ‎Also‎, ‎we expand weakly increasing mappings of S-contractive for two self-mappings and prove some common fixed point theorems with supported examples in complete partial b-metric spaces $(\Re‎, ‎p_{b}^{c})$‎.

In this paper, we first generalized the weighted versions of determinants, permanents and the generalized inverses of rectangular matrices. We also investigate some of their algebraic properties. As a by product of the above investigation, we then present a determinantal representation for the general and Moore-Penrose inverses which satisfy on certain conditions. Finally, we give a general algorithm for determining the inverse of some certain class of the rectangular matrices defined based on weighted determinants.

Considering the $e$-kernel defined by \"{O}zko\c{c} and Ayhan [18] in a topological space, a new type of generalized closed set is studied through this article. The aim of this paper is to introduce a new class of sets called $ge\Lambda$-closed sets and $ge\Lambda$-open sets in a topological space and to study their properties and characterizations.

In this note, we introduce the concept of topologically simple semihypergroup and determine when topological simplicity of a complete subsemihypergroup of a semihypergroup implies its simplicity from algebraic point of view.

‎In this paper‎, ‎we derive the general expression for the entries of the positive integer powers of the Min matrix $A=[\text{min}\{i,j\}];\; i,j=1,2,\cdots,n$ of arbitrary order‎. ‎Also‎, ‎we give Maple 18 procedures in order to verify our calculations‎.