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REMARKS ON VALUE SHARING OF CERTAIN DIFFERENTIAL POLYNOMIALS OF MEROMORPHIC FUNCTIONS

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  28 August 2014

XIAO-MIN LI  and
HONG-XUN YI
XIAO-MIN LI*
Affiliation:
Department of Mathematics, Ocean University of China, Qingdao, Shandong 266100, PR China email [email protected]
HONG-XUN YI
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong 250100, PR China email [email protected]
*
✉[email protected]
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Abstract

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We use Zalcman’s lemma to study a uniqueness question for meromorphic functions where certain associated nonlinear differential polynomials share a nonzero value. The results in this paper extend Theorem 1 in Yang and Hua [‘Uniqueness and value-sharing of meromorphic functions’, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395–406] and Theorem 1 in Fang [‘Uniqueness and value sharing of entire functions’, Comput. Math. Appl. 44 (2002), 823–831]. Our reasoning in this paper also corrects a defect in the reasoning in the proof of Theorem 4 in Bhoosnurmath and Dyavanal [‘Uniqueness and value sharing of meromorphic functions’, Comput. Math. Appl. 53 (2007), 1191–1205].

Keywords

meromorphic functionsshared valuesdifferential polynomialsuniqueness theorems

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory 30D30: Meromorphic functions, general theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 3 , December 2014 , pp. 427 - 443
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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