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

2014/12/29 by Kuldeep Singh Charak, Charak, Kuldeep Singh, Virender Singh +1
Mathematics · #30D35 #30D45 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1412.8271

openalex publication_date 2014/12/29 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove two normality criteria for a family of meromorphic\nfunctions. The first criterion extends a result of Fang and Zalcman[Normal\nfamilies and shared values of meromorphic functions II, Comput. Methods Funct.\nTheory, 1(2001), 289 - 299] to a bigger class of differential polynomials\nwhereas the second one leads to some counterexamples to the converse of the\nBloch's principle.\n

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