Best Proximity Point Results in G -Metric Spaces

Abstract

$G$-metric spaces proved to be a rich source for fixed point theory; however, the best proximity point problem has not been considered in such spaces. The aim of this paper is to introduce certain new classes of proximal contraction mappings and establish the best proximity point theorems for such kind of mappings in $G$-metric spaces. As a consequence of these results, we deduce certain new best proximity and fixed point results. Moreover, we present an example to illustrate the usability of the obtained results.