Chinese Quarterly Journal of Mathematics ›› 1988, Vol. 3 ›› Issue (4): 58-61.
Previous Articles Next Articles
Received:
Online:
Published:
Abstract: In this paper we prove the following theorems: Theorem 1 Let f₁(2) and f₂(z) be in ,where g is the class of meromorphic functions satisfying δ(0)=8(∞)=1, and let a(≠0) be any constant.If 1 (a,f₁)=E₁)(a,f₂),where E₁)(a,f.)={z|f。(z)=a,f{(z)≠0} (i=1,2),then f₁(z)·f₂(2)=a²,unless f₁(2)=f₂(z). Theorem 2 Let f₁(2) and f₂(2) belong to the class s,and let b(≠ 0) be any constant.If E₁(b,fih~)=E₁)(b,fz△),where k is a positive integer, then f₁(t)(2)·f₂()(z)=b²,unless f₁(z)=f₂(z). Corollary. Let f₂(2) and f₂(2) be in g,and let b₁and b₂ be any constants satisfying b₁b₂≠0,b²≠b2. If (i=1,2) then f₁(z)=f₂(z). These results improve some theorems due to Xiong Qinglai,Yang Le Xie Huichun,Yi Hongxun and other authors.
仪洪勋. 关于亚纯函数族的唯一性[J]. Chinese Quarterly Journal of Mathematics, 1988, 3(4): 58-61.
/ Recommend
URL: https://sxjk.magtechjournal.com/EN/
https://sxjk.magtechjournal.com/EN/Y1988/V3/I4/58