Endpoints of multi-valued weak contractions on the metric space valued in partially ordered groups

TL;DR

This paper extends the theory of cone metric spaces to metric spaces valued in partially ordered groups, establishing endpoint theorems for multi-valued weak contractions and advancing fixed point and endpoint theory.

Contribution

It introduces a new framework of metric spaces valued in partially ordered groups and proves endpoint theorems within this setting, extending prior cone metric space results.

Findings

Established endpoint theorems for multi-valued weak contractions

Extended cone metric space theory to partially ordered groups

Generalized fixed point and endpoint results

Abstract

We introduce the metric space valued in partially ordered groups, and define the convergence of sequences and the multi-valued weak contractions, etc., on the space. We then establish endpoint theorems for the defined maps. Our contributions extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).