# A uniqueness problem for entire functions related to Bruck's conjecture

## TL;DR

This paper proves a normal family criterion for meromorphic functions and applies it to establish a new uniqueness theorem for entire functions related to Bruck's conjecture, improving previous results with a novel method.

## Contribution

It introduces a new approach combining normal family theory and Nevanlinna theory to prove a stronger uniqueness theorem for entire functions related to Bruck's conjecture.

## Key findings

- Established a new normality criterion for meromorphic functions.
- Proved a stronger uniqueness theorem for entire functions.
- Improved previous results by using a different methodological approach.

## Abstract

In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Bruck. The above uniqueness theorem is an improvement of a problem studied by L. Z. Yang et. al [14]. However, our method differs the method of L. Z. Yang et. al [14]. We mainly use normal family theory and combine it with Nevanlinna theory instead of using only the Nevanlinna theory as in [14].