New classes of certain analytic functions concerned with subordinations

Breaz, Nicoleta and Owa, Shigeyoshi



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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Breaz, Nicoleta, Owa, Shigeyoshi