Meromorphic functions share three values with their difference operators

TL;DR

This paper proves a conjecture about meromorphic functions sharing three values with their difference operators, confirming it for finite order functions and extending previous results from entire to meromorphic functions.

Contribution

It establishes the conjecture for finite order meromorphic functions and generalizes earlier results from entire to meromorphic functions.

Findings

Conjecture confirmed for finite order meromorphic functions

Generalization from entire to meromorphic functions

Advances the understanding of value sharing in difference operators

Abstract

In the work, we focus on a conjecture due to Z.X. Chen and H.X. Yi[1] which is concerning the uniqueness problem of meromorphic functions share three distinct values with their difference operators. We prove that the conjecture is right for meromorphic function of finite order. Meanwhile, a result of J. Zhang and L.W. Liao[10] is generalized from entire functions to meromorphic functions.