Coupled coincidence point theorems for nonlinear contractions in partially ordered metric spaces

TL;DR

This paper establishes new coupled coincidence and fixed point theorems for nonlinear operators in partially ordered metric spaces, generalizing previous results and encompassing recent related theorems.

Contribution

It introduces generalized coupled fixed point theorems for mixed g-monotone nonlinear operators, extending prior work in partially ordered metric spaces.

Findings

Generalized coupled coincidence point theorems established

Includes several recent results as special cases

Extends previous fixed point theorems in the literature

Abstract

We obtain coupled coincidence and coupled common fixed point theorems for mixed $g$-monotone nonlinear operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. Our results are generalizations of recent coincidence point theorems due to Lakshmikantham and \' Ciri\' c [Lakshmikantham, V., \' Ciri\' c, L., \textit{Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces}, Nonlinear Anal. \textbf{70} (2009), 4341-4349], of coupled fixed point theorems established by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and also include as particular cases several related results in very recent literature.