On Orthogonal Partial  b -Metric Spaces with an Application

Khalil Javed,Muhammad Arshad,Hassen Aydi,Fahim Uddin,Xiaolong Qin

doi:10.1155/2021/6692063

Abstract

In this paper, we initiate the concept of orthogonal partial b -metric spaces. We ensure the existence of a unique fixed point for some orthogonal contractive type mappings. Some useful examples are given, and an application is also provided in support of the obtained results.

Highlights

A natural question is that, under what conditions on κ and U􏽥 does a fixed point exist? eorems which establish the existence of such points are called fixed point theorems. ese results allow us to find the existence of solutions that satisfy certain conditions for operator equations
A lot of fixed point theorems have been investigated in partial spaces
Eshaghi Gordji et al [21] initiated the concept of orthogonal sets and gave an extension of the Banach contraction principle

Summary

Introduction

A natural question is that, under what conditions on κ and U􏽥 does a fixed point exist? eorems which establish the existence (and uniqueness) of such points are called fixed point theorems. ese results allow us to find the existence of solutions that satisfy certain conditions for operator equations. E purpose of this paper is to improve and generalize the concept of an orthogonal contraction in the sense of metric spaces due to Gordji et al [22]. We introduce the concept of an orthogonal partial b-metric and establish some fixed point theorems for related contractions. En, ζ∗ is said as a ρ-metric on U􏽥 and (U􏽥 , ζ∗) is said as a ρ-M.S. In 2014, Shukla [23] introduced the following concept of partial b-metric spaces (in short, ρb-M.Ss) and proved some fixed point results.

Results

Conclusion