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REMARKS ON VALUE SHARING OF CERTAIN DIFFERENTIAL POLYNOMIALS OF MEROMORPHIC FUNCTIONS

Published online by Cambridge University Press:  28 August 2014

XIAO-MIN LI*
Affiliation:
Department of Mathematics, Ocean University of China, Qingdao, Shandong 266100, PR China email lixiaomin@ouc.edu.cn
HONG-XUN YI
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong 250100, PR China email hxyi@sdu.edu.cn
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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].

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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