On coincidence point results of a pair of rational type contractions in quasi-symmetric spaces

Ahmed H. Soliman,Angelamaria Cardone

doi:10.1080/23311835.2017.1301181

Ahmed H. Soliman, Angelamaria Cardone

Open Access

https://doi.org/10.1080/23311835.2017.1301181

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Abstract

In Almeida, Roldan-Lopez-de-Hierro and Sadarangani (2015) proved that whenever T is a rational type contraction mapping from a complete metric space into itself, then T has a unique fixed point. In this work, we establish some coincidence and common point theorems for a pair of rational type contractions in quasi-symmetric spaces.

Highlights

Introduction and preliminariesIt is significant that the prominent contraction principle is a remarkable outcome in fixed point area which has been utilized broadly in numerous fields
In cutting edge years many authors have talked about various ideas of generalized metric spaces, quasi metric, dislocated metric, dislocated quasi metric, symmetric space and quasi-symmetric space in different ways
Metric spaces and contractive conditions naturally arise for several of these problems. we investigate the fixed points of a new generalization of metric spaces called quasi-symmetric spaces in order to extend the theory of fixed points due to Banach and introduce a new fixed point result in the space of quasi-symmetric spaces

Summary

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In cutting edge years many authors have talked about various ideas of generalized metric spaces, quasi metric, dislocated metric, dislocated quasi metric, symmetric space and quasi-symmetric space (see, Hitzler, 2001; Kumari, 2012; Sarma & Kumari, 2012; Schroeder, 1999; Shen & Lu, 2010) in different ways. It was not immediately observed that such spaces may fail to satisfy properties of metric spaces such as a unique limit of convergence sequence, every convergent sequence is a Cauchy sequence and other things. In some of last papers, the authors implicitly used some of properties of metric spaces, so that their results were inaccurate. One of generalized metric spaces which will be under consideration in this paper is quasi-symmetric spaces.

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