An extension of a normality criterion leading to a counterexample to the converse of Bloch's principle
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In this paper, a criterion for normality of a family of meromorphic functions involving differential polynomials is obtained which generalizes a result of Deng et al. (J. Aust. Math. Soc. 91 (2011), 313--322). As a consequence, a counterexample to the converse of Bloch's principle is also obtained. In addition, we prove some normality criterion generalizing a result of Chen et al. (Acta Math. Sci. 36 (2016), 87--93). Wherever possible, examples are provided to demonstrate sharpness of results.
Abstract
In this paper, a criterion for normality of a family of meromorphic functions involving differential polynomials is obtained which generalizes a result of Deng et al. (J. Aust. Math. Soc. 91 (2011), 313--322). As a consequence, a counterexample to the converse of Bloch's principle is also obtained. In addition, we prove some normality criterion generalizing a result of Chen et al. (Acta Math. Sci. 36 (2016), 87--93). Wherever possible, examples are provided to demonstrate sharpness of results.