Summary: We extend the coupled fixed point theorems for a mixed monotone mapping
in partially ordered metric spaces established by T. G. Bhaskar
and V. Lakshmikantham
[Nonlinear Anal., Theory Methods Appl. 65, No. 7, 1379–1393 (2006; Zbl 1106.47047
)]. An application to nonlinear integral equations is also given to illustrate our results.