On Best Proximity Points of Generalized Almost-F-Contraction Mappings

Mahdi Salamatbakhsh,Robab Hamlbarani Haghi

doi:10.22342/jims.25.1.532.16-23

Mahdi Salamatbakhsh, Robab Hamlbarani Haghi

Open Access

https://doi.org/10.22342/jims.25.1.532.16-23

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Abstract

We provide some results about best proximity points of generalized almost-$F$-contraction mappings in metric spaces which generalize and extend recent fixed point theorems. Also, we give an example to illustrate our main result.

Highlights

Fixed point theory focusses on the strategies for solving non-linear equations of the kind T x = x in which T is a self mapping defined on a subset of a metric space
For non self mapping, we try to find an approximate solution for the equation
It should be noted that best proximity point theorems furnish an approximate solution to the mentioned equation when T has no fixed point

Summary

Introduction

For non self mapping, we try to find an approximate solution for the equation. It should be noted that best proximity point theorems furnish an approximate solution to the mentioned equation when T has no fixed point. In [1], the authors introduced the F −Suzuki contraction mappings and proved an existence and uniqueness theorem of fixed point. Following this direction of research and motivated by the works of [1, 3], 2000 Mathematics Subject Classification: 47H10, 54H25, 37C25. We introduce the new class of generalized F −Suzuki contractions and prove a best proximity point theorem concerning such contractions. An example is given to illustrate the usability of the new theory

Main Results

Then by

Then all condition of Theorem