  In this paper we introduce FG- coupled fixed point, which is a generalization
of coupled fixed point for nonlinear mappings in partially ordered complete
metric spaces. We discuss existence and uniqueness theorems of FG- coupled
fixed points for different contractive mappings. Our theorems generalizes the
results of Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V.
Lakshmikantham; Fixed point theorems in partially ordered metric spaces and
applications; Nonlinear Analysis 65 (2006) 1379 -1393].
