Fixed Point Theorems for Almost Z-Contractions with an Application

Huseyin Isik,Nurcan Gungor,Sun Jang,Choonkil Park

doi:10.3390/math6030037

Huseyin Isik, Nurcan Gungor + Show 2 more

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https://doi.org/10.3390/math6030037

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Abstract

In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results.

Highlights

Introduction and PreliminariesIn 1922, Banach [1] initiated studies of metrical fixed points by using contractive mappings in a complete metric space
Since fixed point theory has been a focus of attention because of its application potential in mathematical analysis and other disciplines
Berinde [2] proved that every almost contraction mapping defined on a complete metric space has at least one fixed point

Summary

Introduction

Introduction and PreliminariesIn 1922, Banach [1] initiated studies of metrical fixed points by using contractive mappings in a complete metric space. Berinde [2] proved that every almost contraction mapping defined on a complete metric space has at least one fixed point. Let ( X, d) be a complete metric space and T : X → X be a Z-contraction with respect to a function ζ satisfying certain conditions, that is, ζ (d( Tx, Ty), d( x, y)) ≥ 0 for all x, y ∈ X.

Results

Conclusion