Fixed Point of Generalized Weak Contraction in  b -Metric Spaces

Maryam Iqbal,Afshan Batool,Manuel De La Sen,Ozgur Ege,Santosh Kumar

doi:10.1155/2021/2042162

Fixed Point of Generalized Weak Contraction in b -Metric Spaces

Maryam Iqbal, Afshan Batool + Show 3 more

Open Access

https://doi.org/10.1155/2021/2042162

Copy DOI

Abstract

In this manuscript, a class of generalized ψ , α , β -weak contraction is introduced and some fixed point theorems in the framework of b -metric space are proved. The result presented in this paper generalizes some of the earlier results in the existing literature. Further, some examples and an application are provided to illustrate our main result.

Highlights

Introduction and PreliminariesFixed point theory plays a vital role in the development of nonlinear functional analysis
Banach contraction principle is one of the most important results in fixed point theory introduced by great Polish mathematician Stefan Banach [1]
In 2008, Dutta and Choudhury [25] gave a generalization of weakly contractive mapping by defining ðψ, φÞ-weak contraction in complete metric spaces

Summary

Introduction

Introduction and PreliminariesFixed point theory plays a vital role in the development of nonlinear functional analysis. In 2008, Dutta and Choudhury [25] gave a generalization of weakly contractive mapping by defining ðψ, φÞ-weak contraction in complete metric spaces. Let ðX, dÞ be a complete metric space and T and R are generalized φ -weakly contractive self-maps on X.

Results

Conclusion