Coincidence point theorems for $\varphi$-$\psi$-contraction mappings in metric spaces involving a graph

Abstract

Some new coupled coincidence and coupled common fixed point theorems for ϕ − ψ−contraction mappings are established. We have also an application to some integral system to support the results.

A brief study concerning rational type contraction via a digraph and deformation of an elastic beam

“…Suantai et al [8] studied firstly coincidence coupled f p results of θ − ψ−contractions maps in M SW G. Yolacan et al [15] considered new findings for coupled coincidence point and coupled f p of ϕ − ψ−contraction maps on M SW G. Rao and Kalyani [18] derived coupled f p results for contractive condition of rational type on abstract space. Rao&Kalyani [16] established some existence and uniqueness results for a novel rational contractions on partially ordered metric space.…”

Iteration Scheme for Approximating Fixed Points of G-Nonexpansive Maps on Banach Spaces via a Digraph

“…Jachymski [4] established the conception of 𝐺 −contraction, and unified two notions of graph and fixed point theories. Since then, varied authors have widely probed fixed point theorems in metric space, Banach and Hilbert via graph (see [6], [19][20][21][22][23][24][25]). Aleomraninejad et al [5] achieved several iterative method consequences for 𝐺 −nonexpansiveness and 𝐺 −contractive maps on graphs.…”

A Brief Note Concerning Non-Self Contractions in Banach Spaces Endowed with a Graph

“…The author [1] proved that Ran and Reurings [20] and Edelstein [21] are obtained by [1]. Afterwards, several articles which deal with fixed point theorems for single valued and multivalued mappings in complete metric space with a directed graph appeared [[2]- [10]], [ [15]- [17]].…”