Fixed Point and Homotopy Methods in Cone <b>A</b>-Metric Spaces and Application to the Existence of Solutions to Urysohn Integral Equation

Abstract

The purpose of this article is to introduce an ordered implicit relation that can be used for the existence of fixed points of new contractions defined in cone A-metric spaces. We investigate a fixed-point method for proving the existence of Urysohn integral equation solutions. We prove an homotopy result by the application of obtained fixed-point theorem. The hypothesis is demonstrated with examples.

Keywords

• fixed point
• implicit order relation
• cone \({\textbf{A}}\)-metric space
• implicit contraction