Best proximity points involving F-contraction on a closed ball

Abstract

Abstract. In this paper, we introduce a new idea of best proximity point of F-contraction on a closed ball and obtain new theorems in a complete metric space. That is why this outcome becomes useful for contraction of a mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. Our results that have come into being give a proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.