eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2015-01-14 3 1 7 11 10.12691/tjant-3-1-2 TJANT2015312 article Bhavana Deshpande bhavnadeshpande@yahoo.com 1 Amrish Handa 1 Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India We introduce the concept of generalized weakly compatibility for the pair {F,G} of mappings F,G:X×X-X and also introduce the concept of common fixed point of the mappings F,G:X×X-X. 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. http://pubs.sciepub.com/tjant/3/1/2/tjant-3-1-2.pdf common fixed point generalized symmetric meir-keeler contraction generalized compatibility generalized weakly compatibility commuting mapping