Outcomes of Common Fixed Point Theorems in S-metric Space

Katta Mallaiah,Veladi Srinivas

doi:10.13189/ms.2022.100114

Abstract

In the present paper, we establish the existence of two unique common fixed point theorems with a new contractive condition for four self-mappings in the S-metric space. First, we establish a common fixed-point theorem by using weaker conditions such as compatible mappings of type-(E) and subsequentially continuous mappings. Further, in the next theorem, we use another set of weaker conditions like sub-compatible and sub-sequentially continuous mappings, which are weaker than occasionally weak compatible mappings. Moreover, it is observed that the mappings in these two theorems are sub-sequentially continuous, but these mappings are neither continuous nor reciprocally continuous mappings. These two results will extend and generalize the existing results of [7] and [9] in the S-metric space. Furthermore, we also provide some suitable examples to justify our outcomes.

Highlights

Before we prove our theorem, we’ll discuss some definitions and examples.The Metric space theory was developed in a wide range in the field of mathematics
In the present paper, we establish the existence of two unique common fixed point theorems with a new contractive condition for four self-mappings in the S-metric space
We establish a common fixed-point theorem by using weaker conditions such as compatible mappings of type-(E) and subsequentially continuous mappings

Summary

Introduction

Before we prove our theorem, we’ll discuss some definitions and examples. The Metric space theory was developed in a wide range in the field of mathematics. S-metric space emerges as a generalization of a metric space. For the past several years, the concept of commutative, compatibility, different types of compatible mappings like compatible type-A, type-B, type-C, and type-P became highly significant due to the establishment of many fixed point theorems in different spaces.

PRELIMINARIES

Theorem

EXAMPLE

CONCLUSION