Abstract
Let
X
be a non-empty set and
F
:
X
×
X
→
X
be a given mapping. An element
(
x
,
y
)
∈
X
×
X
is said to be a coupled fixed point of the mapping
F
if
F
(
x
,
y
)
=
x
and
F
(
y
,
x
)
=
y
. In this paper, we consider the case when
X
is a complete metric space endowed with a partial order. We define generalized Meir–Keeler type functions and we prove some coupled fixed point theorems under a generalized Meir–Keeler contractive condition. Some applications of our obtained results are given. The presented theorems extend and complement the recent fixed point theorems due to Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393].