Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25)

Ni̇hal Yilmaz Özgür,Ni̇hal Taş

doi:10.1007/s40096-016-0199-4

Abstract

Recently, S-metric spaces are introduced as a generalization of metric spaces. In this paper, we consider the relationships between of an S-metric space and a metric space, and give an example of an S-metric which does not generate a metric. Then, we introduce new contractive mappings on S-metric spaces and investigate relationships among them by counterexamples. In addition, we obtain new fixed point theorems on S-metric spaces.

Highlights

Sedghi, Shobe, and Aliouche have defined the concept of an S-metric space as a generalization of a metric space in [14] as follows: Definition 1 [14] Let X be a nonempty set, and S : X3 ! 1⁄20; 1Þ be a function satisfying the following conditions for all x; y; z; a 2 X : 1. Sðx; y; zÞ 1⁄4 0 if and only if x 1⁄4 y 1⁄4 z, 2
Recently, S-metric spaces are introduced as a generalization of metric spaces
We give the relationship between the Rhoades’ condition ðR25Þ and ðS25Þ: Proposition 1 Let (X, d) be a complete metric space, ðX; SdÞ be the S-metric space obtained by the S-metric generated by d, and T be a self-mapping of X

Summary

ORIGINAL RESEARCH

Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25). This article is published with open access at Springerlink.com

Introduction

For x

Some applications of contractive mappings on Smetric spaces

Suppose that p!