Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction

Abstract

We introduce the concept of generalized weakly compatibility for the pair {F,G} of mappings , :and also introduce the concept of common fixed point of the mappings , :We establish a common fixed point theorem for generalized weakly compatible pair of mappings , :F G X X X × → without mixed monotone property of any mapping under generalized symmetric Meir-Keeler contraction on a non complete metric space, which is not partially ordered. An example supporting to our result has also been cited. We improve, extend and generalize several known results.