carpathian_2017_33_2_153_160_001

New classes of certain analytic functions concerned with subordinations

Breaz, Nicoleta and Owa, Shigeyoshi

Abstract

carpathian_2017_33_2_153_160_abstract

Issue no: Vol 33/2017 no. 2 Tags: Analytic function, starlike function of order $\alpha$, subordination

Description
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Let $\mathcal{A}$ be the class of analytic functions $f(z)$ in the open unit disk $\mathbb{U}$ which satisfy $f(0)=0$ and $f'(0) = 1$ . Applying the extremal function for the subclass $\mathcal{S}^{*}(\alpha)$ of $\mathcal{A}$ , new classes $\mathcal{P}^{*}(\alpha)$ and $\mathcal{Q}^{*}(\alpha)$ are considered using certain subordinations. The object of the present paper is to discuss some interesting properties for $f(z)$ belonging to the classes $\mathcal{P}^{*}(\alpha)$ and $\mathcal{Q}^{*}(\alpha)$ .

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Author(s)	Breaz, Nicoleta, Owa, Shigeyoshi