In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance. تفاصيل المقالة

‎Let $S$ be an inverse semigroup with the set of idempotents $E$‎.We prove that the semigroup algebra $\ell^{1}(S)$ is always‎‎$2n$-weakly module amenable as an $\ell^{1}(E)$-module‎, ‎for any‎‎$n\in \mathbb{N}$‎, ‎where $E$ acts on $S$ trivially from the left‎‎and by multiplication from the right‎. ‎Our proof is based on a common fixed point property for semigroups‎. تفاصيل المقالة

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. تفاصيل المقالة

‎Best proximity point‎ ‎theorems for self-mappings were investigated with different‎ ‎conditions on spaces for contraction mappings‎. ‎In this‎ ‎paper‎, ‎we prove best proximity point theorems for proximal $\mathcal{F}^{*}$-weak contraction mappings‎. تفاصيل المقالة

‎In the present work‎, ‎Banach and Kannan integral type contractions in metric spaces endowed with a graph are considered and‎ ‎the existence and uniqueness of best proximity points for mappings satisfying in these contractions are proved‎. تفاصيل المقالة

‎The underlying aim of this paper is first to state the cyclic‎‎version of $\mathcal{J}$-integral Banach type contractive mappings introduced by Fallahi‎, ‎Ghahramani and Soleimani Rad‎‎[Integral type contractions in partially ordered metric spaces and best proximity point‎, ‎Iran‎. ‎J‎. ‎Sci‎. ‎Technol‎. ‎Trans‎. ‎Sci‎. ‎44 (2020)‎, ‎177-183]‎ ‎and second to show the existence of best proximity points for such contractive mappings in a metric space with a graph‎, ‎which can entail a large number of former best proximity point results‎. ‎One fundamental issue that can be distinguished between this work and previous researches is that it can also involve all of results stated by taking comparable and $\vartheta$-close elements‎. تفاصيل المقالة