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.

Keywords: Common fixed point; coupled coincidence fixed point; $b$-metric space; $G$-metric space; generalized $b$-metric space.

MSC: 54H25, 47H10, 54E50

Pages:  190$-$201     

Volume  66 ,  Issue  2 ,  2014