Normal Criterion Concerning Shared Values

Normal Criterion Concerning Shared Values

We study normal criterion of meromorphic functions shared values, we obtain the following. Let F be a family of meromorphic functions in a domain D, such that function f∈F has zeros of multiplicity at least 2, there exists nonzero complex numbers bf,cf depending on f satisfying (i)  bf/cf is a const...

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Main Authors: Wei Chen, Yingying Zhang, Jiwen Zeng, Honggen Tian
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/312324
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spelling doaj-eb120a2880914addb8243ef0dce016f92020-11-24T20:47:31ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/312324312324Normal Criterion Concerning Shared ValuesWei Chen0Yingying Zhang1Jiwen Zeng2Honggen Tian3School of Mathematical Sciences, Xinjiang Normal University, Xinjiang, Urumqi 830054, ChinaSchool of Mathematical Sciences, Xinjiang Normal University, Xinjiang, Urumqi 830054, ChinaSchool of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361105, ChinaSchool of Mathematical Sciences, Xinjiang Normal University, Xinjiang, Urumqi 830054, ChinaWe study normal criterion of meromorphic functions shared values, we obtain the following. Let F be a family of meromorphic functions in a domain D, such that function f∈F has zeros of multiplicity at least 2, there exists nonzero complex numbers bf,cf depending on f satisfying (i)  bf/cf is a constant;  (ii)min {σ(0,bf),σ(0,cf),σ(bf,cf)≥m} for some m>0;  (iii)  (1/cfk-1)(f′)k(z)+f(z)≠bfk/cfk-1 or (1/cfk-1)(f′)k(z)+f(z)=bfk/cfk-1⇒f(z)=bf, then F is normal. These results improve some earlier previous results.http://dx.doi.org/10.1155/2012/312324
collection DOAJ
language English
format Article
sources DOAJ
author Wei Chen
Yingying Zhang
Jiwen Zeng
Honggen Tian
spellingShingle Wei Chen
Yingying Zhang
Jiwen Zeng
Honggen Tian
Normal Criterion Concerning Shared Values
Journal of Applied Mathematics
author_facet Wei Chen
Yingying Zhang
Jiwen Zeng
Honggen Tian
author_sort Wei Chen
title Normal Criterion Concerning Shared Values
title_short Normal Criterion Concerning Shared Values
title_full Normal Criterion Concerning Shared Values
title_fullStr Normal Criterion Concerning Shared Values
title_full_unstemmed Normal Criterion Concerning Shared Values
title_sort normal criterion concerning shared values
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description We study normal criterion of meromorphic functions shared values, we obtain the following. Let F be a family of meromorphic functions in a domain D, such that function f∈F has zeros of multiplicity at least 2, there exists nonzero complex numbers bf,cf depending on f satisfying (i)  bf/cf is a constant;  (ii)min {σ(0,bf),σ(0,cf),σ(bf,cf)≥m} for some m>0;  (iii)  (1/cfk-1)(f′)k(z)+f(z)≠bfk/cfk-1 or (1/cfk-1)(f′)k(z)+f(z)=bfk/cfk-1⇒f(z)=bf, then F is normal. These results improve some earlier previous results.
url http://dx.doi.org/10.1155/2012/312324
work_keys_str_mv AT weichen normalcriterionconcerningsharedvalues
AT yingyingzhang normalcriterionconcerningsharedvalues
AT jiwenzeng normalcriterionconcerningsharedvalues
AT honggentian normalcriterionconcerningsharedvalues
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