Best proximity point of α-η-type generalized F-proximal contractions in modular metric spaces

Abstract

The purpose of this paper is to present a study of $ \alpha $-$ \eta $-type generalized $ F $-proximal contraction mappings in the framework of modular metric spaces and to prove some best proximity point theorems for these types of mappings. Some examples are given to show the validity of our results. We also apply our results to establish the existence of solutions for a certain type of non-linear integral equation.

Keywords

• best proximity point
• modular metric space
• generalized $ f $-proximal contractions
• uniform approximation