AN APPLICATION OF CARATHEODORY FUNCTIONS

Year 2017, Volume: 5 Issue: 2, 19 - 23, 15.10.2017

Shigeyoshi Owa

Abstract

Let $\mathcal{P}(\alpha)$ be the class of functions $p(z)$ which are Carath\'eodory functions of order $\alpha \,(0 \leqq \alpha < 1)$ in the open unit disk $\mathbb{U}$. In view of the extremal function $L_0(\alpha;z)$ for the class $\mathcal{P}(\alpha)$, a new class $\mathcal{Q}(\beta)$ of functions $q(z)$ is introduced. The object of the present paper is to discuss some interesting coefficient inequalities for $q(z)$ in the class $\mathcal{Q}(\beta)$.

Keywords

Analytic function, Carath\'eodory function, extremal function, coefficient inequality

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