An order theoretic approach in fixed point theory

TL;DR

This paper develops an order theoretic framework to establish the existence of coupled fixed points for certain mappings in preordered quasi-pseudometric spaces, introducing new concepts like left-weakly related mappings.

Contribution

It introduces a novel order theoretic approach and defines new classes of mappings to study coupled fixed points in preordered quasi-pseudometric spaces.

Findings

Existence of coupled fixed points for order preserving mappings.

Introduction of left-weakly and right-weakly related mappings.

Results for common coupled fixed points in preordered spaces.

Abstract

In the present article, we show the existence of a coupled fixed point for an order preserving mapping in a preordered left K-complete quasi-pseudometric space using a preorder induced by an appropriate function. We also define the concept of left-weakly related mappings on a preordered space and discuss common coupled fixed points for two and three left-weakly related mappings in the same space. Similar results are given for right-weakly related mappings, the dual notion of left-weakly related mappings.