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

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

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 LjḂ. 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.