Best proximity point theorems for tricyclic diametrically contractive mappings

Abstract

In this article, we are referring to introducing a new class of mappings called tricyclic diametrically contractive mappings, which are defined as the union of triad nonempty subsets of a metric space. The authors provide necessary and sufficient conditions for the existence of the best proximity point for these mappings.

This new class of mappings extends the theory of traditional diametrically contractive mappings and provides a more general framework for studying fixed points and optimization problems in metric spaces. The best proximity point, which is a particular type of fixed point that is closest to a given point in the metric space, is an important tool for solving optimization problems.

The results provided in this article represent a significant contribution to the field of analysis and its applications. They are expected to have far-reaching implications for the study of fixed points and optimization problems in metric spaces. The new class of tricyclic diametrically contractive mappings and the conditions for the existence of the best proximity point are likely to be of great interest to researchers in mathematics and science, as well as practitioners in various fields that make use of optimization algorithms.