Meromorphic functions partially share three values with their difference operators

TL;DR

This paper proves a strengthened uniqueness theorem for meromorphic functions sharing specific values with their difference operators, partially resolving a conjecture and generalizing earlier results.

Contribution

It provides a simplified proof of a key theorem, strengthens the result, and partially solves Chen-Yi's conjecture, extending previous theorems in the field.

Findings

Established a strengthened uniqueness theorem for meromorphic functions

Partially solved Chen-Yi's conjecture on value sharing

Generalized previous theorems in meromorphic function theory

Abstract

In this paper, we give a simple proof and strengthening of a uniqueness theorem of meromorphic functions which partially share 0, $\infty$ CM and 1 IM with their difference operators. Meanwhile, we partial solve a conjecture given by Chen-Yi in \cite{CY} and generalize some previous theorems in \cite{C, CX}.