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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 28, Issue 1


Entire functions sharing a polynomial with their derivatives and normal families

Jürgen Grahl / Chao Meng
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/anly.2008.0902

Let ƒ be a nonconstant entire function and Q be a nonconstant polynomial. Let M be a positive number and k ≥ 2 be an integer. We prove that if ƒ and ƒ' share Q CM and |ƒ(k) (z)| ≤ M · (1 + |Q(z)|) whenever ƒ(z) = Q(z), then

is constant. Furthermore, we prove the corresponding normality criterion.

Keywords: Shared values; sharing a polynomial; entire function; normal family; Zalcman's lemma

About the article

Received: 2007-04-18

Published Online: 2009-09-25

Published in Print: 2008-01-01

Citation Information: Analysis, Volume 28, Issue 1, Pages 51–61, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1524/anly.2008.0902.

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