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SOME NORMALITY CRITERIA AND A COUNTEREXAMPLE TO THE CONVERSE OF BLOCH’S PRINCIPLE

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  23 November 2016

KULDEEP SINGH CHARAK  and
SHITTAL SHARMA
KULDEEP SINGH CHARAK*
Affiliation:
Department of Mathematics, University of Jammu, Jammu-180 006, India email kscharak7@rediffmail.com
SHITTAL SHARMA
Affiliation:
Department of Mathematics, University of Jammu, Jammu-180 006, India email shittalsharma_mat07@rediffmail.com
*
✉kscharak7@rediffmail.com
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Abstract

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In this paper, we prove some value distribution results which lead to normality criteria for a family of meromorphic functions involving the sharing of a holomorphic function by more general differential polynomials generated by members of the family, and improve some recent results. In particular, the main result of this paper leads to a counterexample to the converse of Bloch’s principle.

Keywords

value distribution theorynormal familiesmeromorphic functionsdifferential polynomialssharing

MSC classification

Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 30D30: Meromorphic functions, general theory 30D45: Bloch functions, normal functions, normal families
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 2 , April 2017 , pp. 238 - 249
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

The work of the second author is supported by University Grants Commission (UGC), India (No. F.17-77/08(SA-1)).

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