Coupled fixed point theorems for mixed monotone mappings and an application to integral equations

In this paper, we extend the coupled fixed point theorems for a mixed monotone mapping F:X×X→XF:X×X→X in partially ordered metric spaces established by Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379–1393]. An application to nonlinear integral equations is also given to illustrate our results.