Abstract

We establish a coupled coincidence point theorem for generalized compatible pair of mappings <TEX>$F,G:X{\times}X{\rightarrow}X$</TEX> under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of <TEX>$F:X{\times}X{\rightarrow}X$</TEX>. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.