BEST PROXIMITY POINT RESULTS IN THE ORTHOGONAL METRIC SPACES - BRIEF REVEW

Abstract

From the moment when the concept of the orthogonal set appeared in 2017, it become an interesting topic for research. Many authors investigated the uniqueness of best proximal point results in different types of metric space \((X, d)\) where \(X\) is an orthogonal set and \(d\) is a metric on \(X\). Investigation of those results goes in two main directions. The first type of investigation direction deals with different metric spaces, such as standard metric space, \(b\)-metric spaces, metriclike spaces, \(b\) metric like spaces, modular spaces, etc. The second direction deals with different types of contraction. Firstly, we present some necessary definitions with many examples for a better understanding of the concept of the orthogonal set. After that, we give an overview of some results in this field and open problems that could be considered.