Fixed Circle Problem for b-Metric Spaces and Application

Abstract

In the present article, the fixed circle problems are discussed on the structure of b?metric space which offer intriguing insight into geometric topological properties. The notion of a new contraction named as J function is introduced and is examined for the existence and uniqueness of fixed circles of self-mappings on b?metric spaces. Additionally, various examples of self-mappings with fixed circles and new outcomes at discontinuity for fixed circles on b?metric spaces are also provided by several cases of self mappings. Further, the main results investigate circumstances that rule out the identity map when a fixed circle exists in a b?metric space. Fixed circles are used in complex analysis, robotics and neural networks to solve problems and model scenarios. In robotics, they set movement limits, while in neural networks, discontinuous maps improve storage capacity and optimize solutions by identifying fixed points. We applied the main result to examine two mappings and demonstrated that it ensures the existence of the common fixed circle, utilizing it to solve optimization problems in b?metric spaces.