Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings

Kapil Jain,Jatinderdeep Kaur

doi:10.3390/axioms10020055

Abstract

The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems.

Highlights

The well-known concept of metric space was introduced by M
Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings
We first define a new class of functions, and we define a new contractive mapping in b-metric spaces as follows

Summary

Introduction

The well-known concept of metric space was introduced by M. Frechet [1] as an extension of usual distance. In the theory of metric space, Banach’s contraction principle [2] is one of the most important theorems and a powerful tool. A mapping T : X → X, where (X, d) is a metric space, is called a contraction mapping if there exists α < 1 such that for all x, y ∈ X, d(Tx, Ty) ≤ αd(x, y). If the metric space (X, d) is complete, T has a unique fixed point. In [3], Kannan proved the following result which gives the fixed point for discontinuous mapping: let T : X → X, be a mapping on a complete metric space (X, d) with

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Conclusion