Further Results about the Normal Family of Meromorphic Functions and Shared Sets

• Journal title : Kyungpook mathematical journal
• Volume 52, Issue 1,  2012, pp.39-47
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2012.52.1.39
Title & Authors
Further Results about the Normal Family of Meromorphic Functions and Shared Sets
Qi, Jianming; Zhang, Guowei; Zhou, Linlin;

Abstract
Let $\small{\mathcal{F}}$ be a family of meromorphic functions in a domain D, and let $\small{k}$, $\small{n({\geq}2)}$ be two positive integers, and let $\small{S=\{a_1,a_2,{\ldots},a_n\}}$, where $\small{a_1}$, $\small{a_2}$, $\small{{\ldots}}$, $\small{a_n}$ are distinct finite complex numbers. If for each $\small{f{\in}\mathcal{F}}$, all zeros of $\small{f}$ have multiplicity at least $\small{k+1}$, $\small{f}$ and $\small{G(f)}$ share the set $\small{S}$ in $\small{D}$, where $\small{G(f)=P(f^{(k)})+H(f)}$ is a differential polynomial of $\small{f}$, then$\small{\mathcal{F}}$ is normal in $\small{D}$.
Keywords
Meromorphic functions;Nevanlinna theory;Normal family;Share value;
Language
English
Cited by
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