Two normality criteria and counterexamples to the converse of Bloch's principle

Kuldeep Singh Charak; Virender Singh

doi:10.2996/kmj/1446210601

Kodai Mathematical Journal

Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991

Two normality criteria and counterexamples to the converse of Bloch's principle

Kuldeep Singh Charak, Virender Singh

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Keywords: Normal families, Meromorphic function, Differential polynomial, Shared value, Small function

JOURNAL FREE ACCESS

2015 Volume 38 Issue 3 Pages 672-686

DOI https://doi.org/10.2996/kmj/1446210601

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Abstract

In this paper, we prove two normality criteria for a family of meromorphic functions. The first criterion extends a result of Fang and Zalcman [Normal families and shared values of meromorphic functions II, Comput. Methods Funct. Theory, 1 (2001), 289-299] to a bigger class of differential polynomials whereas the second one leads to some counterexamples to the converse of the Bloch's principle.

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