Fixed Point Results on Closed Ball in Convex Rectangularb−Metric Spaces and Applications

Abstract

In this paper, the concept of convex rectangular$b-$metric spaces is introduced as a generalization of both convex metric spaces and rectangular$b-$metric spaces. The purpose of this study is to indicate a way of generalizing Mann’s iteration algorithm and a series of fixed point results in rectangular$b-$metric spaces. Furthermore, certain examples are given to support the results. We also study well posedness of fixed point problems of some mappings in convex rectangular$b-$metric spaces, and an application to the dynamic programming is entrusted to manifest the viability of the obtained results. Our results extend comparable results in the existing literature.