Common fixed point theorems for generalized ( ϕ , ψ ) -weak contraction condition in complete metric spaces

Penumarthy Parvateesam Murthy,Kenan Tas,Uma Devi Patel

doi:10.1186/s13660-015-0647-y

Penumarthy Parvateesam Murthy, Kenan Tas + Show 1 more

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https://doi.org/10.1186/s13660-015-0647-y

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Abstract

The intent of this manuscript is to establish some common fixed point theorems in a complete metric space under weak contraction condition for two pairs of discontinuous weak compatible maps. The results proved herein are the generalization of some recent results in literature. We give an example to support our results.

Highlights

One can see in the literature on metric fixed point theory that condition ( . ) has been extended and generalized by fixed point theorists in many ways for obtaining fixed points, common fixed points and, very recently, proximal points in different spaces
The title of this paper implies that the pair of maps in a complete metric space satisfies certain inequality by generalizing the contraction condition of Banach, but the inequality itself does not force the mapping to be continuous
The main purpose of this note is to establish a few common fixed point theorems by generalizing the results of Murthy et al [ ] for two pairs of discontinuous functions in a complete metric space by using a weaker condition than condition ( . ) called (φ, ψ)-weak contraction condition in metric spaces

Summary

Introduction

The title of this paper implies that the pair of maps in a complete metric space satisfies certain inequality by generalizing the contraction condition of Banach, but the inequality itself does not force the mapping to be continuous.

Results

Conclusion