  In this paper we extend the coupled fixed point theorems for mixed monotone
operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V.
Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces
and applications}, Nonlinear Anal. \textbf{65} (2006) 1379-1393] and [N.V.
Luong and N.X. Thuan, \textit{Coupled fixed points in partially ordered metric
spaces and application}, Nonlinear Anal. \textbf{74} (2011) 983-992], by
weakening the involved contractive condition. An example as well an application
to nonlinear Fredholm integral equations are also given in order to illustrate
the effectiveness of our generalizations.
