A Fixed Point Theorem on Partial Metric Spaces of Hyperbolic Type

Abstract

In this research paper, we introduce the concept of partial metric spaces of hyperbolic type. When it comes to hyperbolic spaces, they are mostly studied in the context of metric spaces. A partial metric space is a generalization of a metric space, where self-distance is not necessarily zero. This concept became particularly interesting when Kumar et al. (2017) introduced and studied convex partial metric spaces. His result were useful in defining partial metric spaces of hyperbolic type, which is the kickoff point of our paper. After this, we focus our study in providing a proof of the existence of a fixed point for a non-self-mapping of a specific contracting type that was first introduced by Ćirić (2006). Our result is a generalization of the results of Ćirić and other cited authors. In the end an example is provided. This example serves to illustrate the applicability of our fixed point theorem and shows that results from metric spaces of hyperbolic type can be extended to partial metric spaces of hyperbolic type.