PROXIMAL TYPE CONVERGENCE RESULTS USING IMPLICIT RELATION AND APPLICATIONS

Abstract

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtainedresults. Furthermore, some uniqueness results for proximal contractions are also furnishedwith partial order and graph. Various well-known discoveries in the present state-of-the-artare enhanced, extended, unified, and generalized by our findings. As an application, wegenerate some fixed point results fulfilling a modified contraction and a graph contraction,using the profundity of the established results.