Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction

Bhavana Deshpande^1, and Amrish Handa¹

¹Department of Mathematics Govt. P. G. Arts & Science College Ratlam (M. P.) India

Cite this paper:
Bhavana Deshpande and Amrish Handa. Common Fixed Point Results for Generalized Symmetric Meir-Keeler Contraction. Turkish Journal of Analysis and Number Theory. 2015; 3(1):7-11. doi: 10.12691/tjant-3-1-2

Abstract

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.

Keywords:
common fixed point generalized symmetric meir-keeler contraction generalized compatibility generalized weakly compatibility commuting mapping

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