Differential sandwich theorems for some subclasses of analytic functions associated with linear operator (Q884150)

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scientific article; zbMATH DE number 5163952
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Differential sandwich theorems for some subclasses of analytic functions associated with linear operator
scientific article; zbMATH DE number 5163952

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    Differential sandwich theorems for some subclasses of analytic functions associated with linear operator (English)
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    13 June 2007
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    The authors study on some results related to differential sandwich theorems for some subclasses of analytic functions associated with linear operator. Let \(q_{1}\) and \(q_{2}\) be univalent in \(\Delta=\{z:| z| <1\}\) with \(q_{1}(0)=q_{2}(0)=1\). The authors apply the first order differential subordination and superordination to obtain sufficient conditions for a normalised analytic functions \(f(z)\) with \(f(0)=f'(0)-1=0\) to satisfy \[ q_{1}(z)\prec\dfrac{zf'(z)}{f(z)}\prec q_{2}(z). \] The authors obtain solid 14 theorems with some applications to Carlson-Shaffer operator, Ruscheweyh and Salagean derivatives.
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    analytic
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    univalent
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    convex
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    extreme point
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    starlikeness
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    linear operator
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