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

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