Coincidence best proximity point theorems for proximal Berinde g-cyclic contractions in metric spaces

Chalongchai Klanarong,Inthira Chaiya

doi:10.1186/s13660-021-02547-5

Chalongchai Klanarong, Inthira Chaiya

Open Access

https://doi.org/10.1186/s13660-021-02547-5

Copy DOI

Abstract

In this paper, we introduce the notions of proximal Berinde g-cyclic contractions of two non-self-mappings and proximal Berinde g-contractions, called proximal Berinde g-cyclic contraction of the first and second kind. Coincidence best proximity point theorems for these types of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our main results extend and generalize many existing results in the literature.

Highlights

1 Introduction Fixed point theory has an important role in the study of theory of nonlinear equations
He proved that every weak contraction mapping from a complete metric space X into itself has a fixed point
Fixed point theory has great importance in solving nonlinear equations of the form Jx = x, where J is a self-mapping, if J is a non-self-mapping, it is possible that J has no fixed points

Summary

Introduction

Fixed point theory has an important role in the study of theory of nonlinear equations. Basha [5] proved the existence of the following best proximity point in a complete metric space.

Objectives

Results

Conclusion