FG-coupled fixed point theorems for contractive and generalized quasi-contractive mappings

TL;DR

This paper establishes FG-coupled fixed point theorems for various contractive and quasi-contractive mappings in ordered metric spaces, expanding fixed point theory for both continuous and discontinuous functions.

Contribution

It introduces new FG-coupled fixed point theorems applicable to a broader class of mappings in partially ordered complete metric spaces.

Findings

Existence of FG-coupled fixed points for continuous mappings

Existence of FG-coupled fixed points for discontinuous mappings

Examples illustrating the theorems

Abstract

In this paper we prove FG-coupled fixed point theorems for different contractive mappings and generalized quasi- contractive mappings in partially ordered complete metric spaces. We prove the existence of FG-coupled fixed points of continuous as well as discontinuous mappings. We give some examples to illustrate the results.