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June 2005 On Certain Differential Subordination and its Dominant
Sushma Gupta, Sukhjit Singh
Bull. Belg. Math. Soc. Simon Stevin 12(2): 259-274 (June 2005). DOI: 10.36045/bbms/1117805088

Abstract

Denote by $\cal A'$, the class of functions $f$, analytic in $E$ which satisfy $f(0)=1$. Let $\alpha >0, \beta \in (0,1]$ be real numbers and let $\gamma, {\rm Re} \gamma >0$, be a complex number. For $p, q \in \cal A'$, the authors study the differential subordination of the form $$(p(z))^\alpha \left[1+\frac {\gamma zp'(z)}{p(z)}\right]^\beta \prec(q(z))^\alpha \left[1+\frac {\gamma zq'(z)}{q(z)}\right]^\beta, z\in E,$$ and obtain its best dominant. Its applications to univalent functions are also given.

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Sushma Gupta. Sukhjit Singh. "On Certain Differential Subordination and its Dominant." Bull. Belg. Math. Soc. Simon Stevin 12 (2) 259 - 274, June 2005. https://doi.org/10.36045/bbms/1117805088

Information

Published: June 2005
First available in Project Euclid: 3 June 2005

zbMATH: 1093.30015
MathSciNet: MR2179968
Digital Object Identifier: 10.36045/bbms/1117805088

Subjects:
Primary: 30C45
Secondary: 30C50

Rights: Copyright © 2005 The Belgian Mathematical Society

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Vol.12 • No. 2 • June 2005
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