# Some fixed-circle theorems on metric spaces

## TL;DR

This paper introduces new theorems on the existence and uniqueness of fixed circles in metric spaces, providing geometric insights and illustrative examples to demonstrate their applicability.

## Contribution

It presents novel fixed-circle theorems in metric spaces, expanding fixed-point theory with geometric interpretations and verification through examples.

## Key findings

- Established existence of fixed circles under certain conditions
- Proved uniqueness of fixed circles in specific metric space contexts
- Provided illustrative examples confirming theoretical results

## Abstract

The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We verify our results by illustrative examples.