Coupled fixed point theorems in $G_{b}$-metric spaces

Shaban Sedghi, Nabi Shobkolaei, Jamal Rezaei Roshan and Wasfi Shatanawi

Abstract

T. G. Bhaskar and V. Lakshmikantham [Fixed point theorems
in partially ordered metric spaces and applications, Nonlinear Anal. 65
(2006) 1379--1393], V. Lakshmikantham and
Lj\. B. Ćirić [Coupled fixed point
theorems for nonlinear contractions in partially ordered metric spaces,
Nonlinear Anal. 70 (2009) 4341--4349] introduced the concept of a coupled
coincidence point of a mapping $F$ from $X\times X$ into $X$ and a mapping
$g$ from $X$ into $X$. In this paper we prove a coupled coincidence fixed
point theorem in the setting of a generalized $b$-metric space. Three
examples are presented to verify the effectiveness and applicability of our
main result.