# Common Fixed Point results in Complex valued metric spaces via simulation functions

## TL;DR

This paper introduces complex-valued simulation functions to establish common fixed point theorems in complex metric spaces, with applications to differential equations.

## Contribution

It develops the concept of $ ext{C}$-simulation functions and proves fixed point results in complex metric spaces, extending fixed point theory.

## Key findings

- Established existence and uniqueness of common fixed points
- Provided examples demonstrating the results
- Applied findings to a differential equation problem

## Abstract

In this paper, the notion of $\mathbb{C}$-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via $\mathbb{C}$-simulation functions are studied. Examples are also provided to demonstrate the results. The existence and uniqueness of a first-order periodic differential equation is also obtained as an application of the result.