Meromorphic Functions Sharing a Small Function

We will study meromorphic functions that share a small function, and prove the following result: let f(z) and g(z) be two transcendental meromorphic functions in the complex plane and let n≥11 be a positive integer. Assume that a(z)(≢0) is a common small function with respect to f(z) and g(z). If fn...

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Main Authors: Songmin Wang, Zongsheng Gao
Format: Article
Language:English
Published: Wiley 2007-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2007/60718
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author Songmin Wang
Zongsheng Gao
author_facet Songmin Wang
Zongsheng Gao
author_sort Songmin Wang
collection DOAJ
description We will study meromorphic functions that share a small function, and prove the following result: let f(z) and g(z) be two transcendental meromorphic functions in the complex plane and let n≥11 be a positive integer. Assume that a(z)(≢0) is a common small function with respect to f(z) and g(z). If fnf′ and gng′ share a(z) CM, then either fn(z)f′(z)gn(z)g′(z)≡a2(z), or f(z)≡tg(z) for a constant satisfying tn+1=1. As applications, we give several examples.
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series Abstract and Applied Analysis
spelling doaj-art-1b1e5af113124cda89d3b9d77c3baa912025-08-20T02:02:20ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/6071860718Meromorphic Functions Sharing a Small FunctionSongmin Wang0Zongsheng Gao1LMIB and Department of Mathematics, Beihang University, Beijing 100083, ChinaLMIB and Department of Mathematics, Beihang University, Beijing 100083, ChinaWe will study meromorphic functions that share a small function, and prove the following result: let f(z) and g(z) be two transcendental meromorphic functions in the complex plane and let n≥11 be a positive integer. Assume that a(z)(≢0) is a common small function with respect to f(z) and g(z). If fnf′ and gng′ share a(z) CM, then either fn(z)f′(z)gn(z)g′(z)≡a2(z), or f(z)≡tg(z) for a constant satisfying tn+1=1. As applications, we give several examples.http://dx.doi.org/10.1155/2007/60718
spellingShingle Songmin Wang
Zongsheng Gao
Meromorphic Functions Sharing a Small Function
Abstract and Applied Analysis
title Meromorphic Functions Sharing a Small Function
title_full Meromorphic Functions Sharing a Small Function
title_fullStr Meromorphic Functions Sharing a Small Function
title_full_unstemmed Meromorphic Functions Sharing a Small Function
title_short Meromorphic Functions Sharing a Small Function
title_sort meromorphic functions sharing a small function
url http://dx.doi.org/10.1155/2007/60718
work_keys_str_mv AT songminwang meromorphicfunctionssharingasmallfunction
AT zongshenggao meromorphicfunctionssharingasmallfunction