# Uniqueness of the power of a meromorphic functions with its differential polynomial sharing a set

## TL;DR

This paper investigates the uniqueness of meromorphic functions when their powers and differential polynomials share a set, extending existing results in normal family theory and proposing future research directions.

## Contribution

It introduces new uniqueness criteria for meromorphic functions sharing a set with their differential polynomials, expanding the scope of normal family theory.

## Key findings

- Extended known results in normal family theory
- Established new conditions for function uniqueness
- Posed open questions for future research

## Abstract

This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are posed for future research.