Fixed Point Theorems for Mann’s Iteration Scheme in Convex Gb-Metric Spaces with an Application

Abstract

In this paper, we present a series of fixed point results for Mann’s iteration scheme in the framework of Gb-metric spaces. First, we introduce the concept of convex Gb-metric space by means of a convex structure and Mann’s iteration algorithm is extended to this space. Furthermore, using Mann’s iteration scheme, we prove some fixed point results for several mappings satisfying various suitable conditions on complete convex Gb-metric spaces. Some examples supporting our main results are also presented. We also discuss the well-posedness of the fixed point problems and the P property for given mappings. Moreover, as an application, we apply our main result to prove the existence of the solutions to integral equations.