Pata Zamfirescu Type Fixed-Disc Results with a Proximal Application

TL;DR

This paper introduces new generalized contractive conditions that guarantee the existence of fixed discs or circles for self-mappings in metric spaces, along with the concept of a best proximity circle and applications to non-self-mappings.

Contribution

It presents novel fixed point results involving fixed discs and circles, and introduces the notion of a best proximity circle for non-self-mappings.

Findings

Established conditions for fixed discs and circles in metric spaces.

Introduced the concept of a best proximity circle.

Provided illustrative examples demonstrating the results.

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.