Some Normality Criteria and a Counterexample to the Converse of Bloch's Principle

2015/09/24 by Charak, Kuldeep Singh, Sharma, Shittal · 1 citation
#30D30 #30D35 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.07293

Abstract

In this paper we continue our earlier investigations on normal families of meromorphic functions\citeCS2. Here, we prove some value distribution results which lead to some 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 get some recently known results extended and improved. In particular, the main result of this paper leads to a counterexample to the converse of Bloch's principle.

Cited by

• A Note on Normal Families Concerning Nonexceptional Functions and Differential Polynomials

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