Pata Zamfirescu Type Fixed-Disc Results with a Proximal Application

Abstract

This paper is concerning to the geometric study of fixed points of a self-mapping on a metric space. We establish new generalized contractive conditions which ensure that a self-mapping has a fixed disc or a fixed circle. We introduce the notion of a best proximity circle and explore some proximal contractions for a non-self-mapping as an application. Necessary illustrative examples are presented to highlight the importance of the obtained results.