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Normal Function Related to Shared Sets(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2018年04期
Page:
12-
Research Field:
·数学与计算机科学·
Publishing date:

Info

Title:
Normal Function Related to Shared Sets
Author(s):
Huang Xiaojie1; 2; Liu Zhixiu1; Li Yuntong3
(1.Department of Science,Nanchang Institute of Technology,Nanchang 330099,China)(2.School of Mathematic Sciences,Fudan University,Shanghai 200433,China)(3.Shanxi Railway Institute,Weinan 714000,China)
Keywords:
normal function; normal family; shared set
PACS:
O174.5
DOI:
10.3969/j.issn.1001-4616.2018.04.003
Abstract:
This paper studies the normal conditions of meromorphic function relating to sharing sets by the function and its higher derivatives. By use of Lohwater-Pommerenke’s theorem and Zalcman-Pang’s lemma as well as Nevanlinna theory,it proves that let S1={a1,a2,a3}and S2={b1,b2}be two sets consisting of different finite complex numbers,k≥2 be a positive integer number,if f(z) be a meromorphic function on unit circle domain Δ such that the zeros of f(z)-ai have multiplicity at least k,i=1,2,3 and {z∈Δ|f(z)∈S1}={z∈Δ|f(k)(z)∈S2},then f(z)is a normal function on domain Δ.

References:

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Last Update: 2018-12-30