Some approximate best proximity point results on metric spaces and its applications

Abstract

The aim of this paper is to extend the concept of determining an approximate fixed points (AFP) to determine approximate best proximity points (ABPP) using several contraction mappings, such as weak contraction, Zamfirescu contraction, Ciric-Reich-Rus contraction and the related consequences in metric spaces. In particular, we study the existence (qualitative results) and the diameter (quantitative results) of ABPP on metric spaces. Moreover, a few examples are provided to illustrate our results. Furthermore, suitable applications of the main findings are discussed in the domain of differential equations.