Some fixed circle theorems in multiplicative metric spaces

Abstract

The fixed point theory and its relevance to diverse scientific domains are widely recognized. The field of fixed point theory has incorporated a novel geometric concept known as the fixed circle problem. This paper establishes the existence and uniqueness theorems concerning fixed circles of self mappings on multiplicative metric spaces. We introduced the Caristi type contraction in the framework of multiplicative metric spaces and utilizing this concept, established theorems guaranteeing the existence of fixed circles. We validate our findings through illustrative examples.