A new comprehensive class of analytic functions defined by multiplier transformation (Q409909)
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scientific article; zbMATH DE number 6024296
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new comprehensive class of analytic functions defined by multiplier transformation |
scientific article; zbMATH DE number 6024296 |
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A new comprehensive class of analytic functions defined by multiplier transformation (English)
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15 April 2012
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differential subordination
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multiplier transformation
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convex functions
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best dominant
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differential operator
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For \(\delta\in[0,1)\), \(\lambda,l\geq 0\) and \(m\geq 1\) an integer, the author derives several differential subordination results for functions \(f(z)=z+a_{n+1}z^{n+1}+\cdots \) to satisfy \(\text{Re} ( I(m, \lambda,l)f (z))'>\delta\) or \(( I(m, \lambda,l)f (z))' \prec g(z)\) for some suitable \(g\), where \(I(m,\lambda,l)f(z)\) is the transformation defined by NEWLINE\[NEWLINE I(m,\lambda,l)f(z)=z+\sum^\infty_{j=n+1}\left((\lambda(j-1)+l+1)/(l+1)\right)^ma_jz^j .NEWLINE\]NEWLINE Some other related results are also proved.
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