Normal families of meromorphic functions sharing a holomorphic function and the converse of the Bloch principle

Yunbo, Jiang; Гао, Зонгшенг

doi:10.1016/s0252-9602(12)60119-2

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Introduction and Main Results2

Counterexamples To the Converse Of The Bloch's Principle1

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Cited by 8 publications

(4 citation statements)

References 14 publications

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“…Further, one can ask what can be said about normality of family F if set S in Corollary 1.5 has cardinality equal to one. In this direction, we prove the following result which in turn extends the results of Yunbo and Zongsheng [13], Meng and Hu [6], Charak and Sharma [2] and Sun [10].…”

Section: Introduction and Main Resultssupporting

confidence: 80%

Normality criteria concerning composite meromorphic functions

Singh,

Charak

2015

Preprint

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Section: Introduction and Main Resultssupporting

confidence: 80%

Normality criteria concerning composite meromorphic functions

Singh,

Charak

2015

Preprint

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“…Like Bloch's principle, its converse is not true. For counterexamples one can see [2] [5], [10], [11], [14], [17], and [18].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Some Normality Criteria and A counterexample to the Converse of Bloch’s Principle

Charak¹,

Sharma²

2016

Bull. Aust. Math. Soc.

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Abstract. In this paper we continue our earlier investigations on normal families of meromorphic functions [4]. 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.

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“…Like Bloch's principle, its converse is not true. For counterexamples one can see [1], [8], [10], [16], [18], [20]. In order to construct counterexamples to the converse, one needs to prove a suitable normality criterion.…”

Section: Counterexamples To the Converse Of The Bloch's Principlementioning

confidence: 99%

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

Charak¹,

Singh²

2015

Kodai Math. J.

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

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Normal families of meromorphic functions sharing a holomorphic function and the converse of the Bloch principle

Cited by 8 publications

References 14 publications

Normality criteria concerning composite meromorphic functions

Normality criteria concerning composite meromorphic functions

Some Normality Criteria and A counterexample to the Converse of Bloch’s Principle

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

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