Quasi-normal Family of Meromorphic Functions Whose Certain Type of Differential Polynomials Have No Zeros

• 作者: Jian Ming CHANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（8）
• 页码范围: 1267-1277
• 页数: 11页
• 语种: 英文

摘要

Define the differential operators φn for n ∈ N inductively by φ1[f](z)=f(z)and φn+1[f](z)=f(z)φn[f](z)+d/dzφn[f](z).For a positive integer k≥2 and a positive number δ,let F be the family of functions f meromorphic on domain D?C such that φk[f](z)≠ 0 and |Res(f,a)-j|≥δ for all j ∈{0,1,...,k-1}and all simple poles a of f in D.Then F is quasi-normal on D of order 1.