# Fixed-disc results via simulation functions

## TL;DR

This paper introduces a novel approach using simulation functions to establish fixed-disc results in metric spaces without requiring strong conditions like completeness or continuity, broadening fixed-point theory applications.

## Contribution

It presents a new method leveraging simulation functions to obtain fixed-disc results under minimal geometric conditions, without assuming completeness or continuity.

## Key findings

- Existence of fixed discs under weaker conditions
- No need for completeness or compactness assumptions
- Applicable to a new class of contractive mappings

## Abstract

In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping.