Journal of Linear and Topological Algebra
Volume:7 Issue: 3, Summer 2018

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spaces. We also provide examples to analyze and support our results.

The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an application, we provide an existence theorem for a coupled elliptic system subject to various two-point boundary conditions.

In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work, we introduce the concept of $A$-fuzzy contractive mappings. Finally, we support our results by some examples.

In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying some generalized contractive type conditions in $b$-metric spaces endowed with graphs and altering distance functions. Finally, some examples are provided to justify the validity of our results.

In this work, we prove some fixed point theorems by using $wt$-distance on b-metric spaces. Our results generalize some fixed point theorems in the literature. Moreover, we introduce $wt_0$-distance and by using the concept of $wt_0$-distance, we obtain some coupled fixed point results in complete b-metric spaces.

In this paper, the notions of a Suzuki-Berinde type $F_{S}$-contraction and a Suzuki-Berinde type $F_{C}^{S}$-contraction are introduced on a $S$-metric space. Using these new notions, a fixed-point theorem is proved on a complete $S$-metric space and a fixed-circle theorem is established on a $S$-metric space. Some examples are given to support the obtained results.

In this paper, we introduce the $ b-(varphi, Gamma)-$graphic contraction on metric space endowed with a graph so that $(M,delta)$ is a metric space, and $V(Gamma)$ is the vertices of $Gamma$ coincides with $M$. We aim to obtain some new fixed-point results for such contractions. We give an example to show that our results generalize some known results.