Generalized c-distance on cone b-metric spaces endowed with a graph and fixed point results

Abstract

The aim of this paper is to present fixed point results of contractive mappings in the framework of cone b-metric spaces endowed with a graph and associated with a generalized c-distance. Some corollaries and an example are presented to support the main result proved herein. Our results unify, extend and generalize various comparable results in the literature.2010 MSC: 46A19; 47H10; 05C20.

Fixed point results with respect to a wt-distance in partially ordered b-metric spaces and its application to nonlinear fourth-order differential equation

“…They showed that under such conditions the conclusions of Banach's fixed point theorem still hold. This fixed point theorem was extended by Nieto and Rodríguez-López [18] and was applied to the periodic boundary value problem (see, e.g., [8,9,13,14,19,20]). A relation on X is called (i) reflexive if x x for all x ∈ X;…”