Value distribution of certain differential polynomials and a counterexample to the converse of Bloch's principle
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In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for certain differential polynomials which lead to some normality criteria involving sharing of holomorphic functions with certain differential polynomials. As a consequence, a counterexample to the converse of the Bloch's principle is also obtained.
Abstract
In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for certain differential polynomials which lead to some normality criteria involving sharing of holomorphic functions with certain differential polynomials. As a consequence, a counterexample to the converse of the Bloch's principle is also obtained.