Existence and Unique Coupled Solution in Sb-Metric Spaces by Rational Contraction with Application

Jelena Vujaković,Shaik Sadik,Stojan Radenović,K P R Rao ,G.n.v Kishore

doi:10.3390/math7040313

Jelena Vujaković, Shaik Sadik + Show 3 more

Open Access

https://doi.org/10.3390/math7040313

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Journal: Mathematics	Publication Date: Mar 28, 2019
Citations: 1	License type: CC BY 4.0

Affiliation: Acharya Nagarjuna University, King Saud University

Abstract

In this paper, we prove a unique common coupled fixed point theorem for two pairs of w-compatible mappings in S b -metric spaces. We also furnish an example to support our main result.

Highlights

In 2012, Sedghi et al [1] introduced the notion of S-metric space and proved several results.Some other authors worked on this (e.g., [2,3,4,5,6])
Sedghi et al [1] defined Sb -metric spaces using the concepts of S and b-metric spaces and proved common fixed point theorem for four maps in Sb -metric spaces
Bhaskar and Lakshmikantham [13] introduced the notion of coupled fixed point and proved some coupled fixed point results as well

Summary

Introduction

In 2012, Sedghi et al [1] introduced the notion of S-metric space and proved several results.Some other authors worked on this (e.g., [2,3,4,5,6]). The aim of this paper is to prove a unique common coupled fixed point theorem for four mappings in Sb -metric spaces. ([1]) A Sb -metric space (X, Sb ) is called complete if every Sb -Cauchy sequence is Sb -convergent in X.

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