FG- coupled fixed point theorems for various contractions in partially ordered metric spaces

TL;DR

This paper introduces FG-coupled fixed points as a generalization of coupled fixed points in ordered metric spaces, providing new existence and uniqueness theorems for various contractive mappings.

Contribution

It extends existing fixed point theorems by defining FG-coupled fixed points and establishing their properties in partially ordered complete metric spaces.

Findings

Generalized fixed point theorems for nonlinear mappings

Existence and uniqueness results for FG-coupled fixed points

Broadened applicability of fixed point theory in ordered metric spaces

Abstract

In this paper we introduce FG- coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG- coupled fixed points for different contractive mappings. Our theorems generalizes the results of Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham; Fixed point theorems in partially ordered metric spaces and applications; Nonlinear Analysis 65 (2006) 1379 -1393].