Meromorphic functions sharing three values im with its linear differential polynomials

Abstract

Mues–Reinders proved that if a non-constant meromorphic function f shares three distinct finite values IM with its Kth (2≤ k≤ 50) linear differential polynomial L(f), then f≡L(f). Frank and Hua proved the same result under a weak condition k≥2. In the present paper, we will prove this result in the case that k = 1.