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- W1971948121 abstract "Abstract In the note, we study the normality of families of meromorphic functions. We consider whether a family of meromorphic functions ℱ is normal in D if, for a normal family <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>G</mml:mi> </mml:math> and for each function <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>f</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>F</mml:mi> </mml:math> , there exists <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>g</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>G</mml:mi> </mml:math> such that <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> implies <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>g</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:msup> <mml:mi>g</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> for two distinct nonzero points <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> , <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:math> and an integer n . An example shows that the condition in our results is best possible. MSC: 30D45, 30D35." @default.
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- W1971948121 date "2013-11-07" @default.
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- W1971948121 title "Some normality criteria for families of meromorphic functions" @default.
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- W1971948121 doi "https://doi.org/10.1186/1029-242x-2013-459" @default.
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