AN APPLICATION OF CARATHEODORY FUNCTIONS

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Konuralp Journal of Mathematics
Volume:5 Issue:2
AN APPLICATION OF CARATHEODORY FUNCTIONS

AN APPLICATION OF CARATHEODORY FUNCTIONS

Authors : Shigeyoshi OWA

Pages : 19-23

View : 40 | Download : 9

Publication Date : 2017-10-15

Article Type : Research Paper

Abstract :Let $\mathcal{P}insert ignore into journalissuearticles values(\alpha);$ be the class of functions $pinsert ignore into journalissuearticles values(z);$ which are Carath\`eodory functions of order $\alpha \insert ignore into journalissuearticles values(0 \leqq \alpha < 1);$ in the open unit disk $\mathbb{U}$. In view of the extremal function $L_0insert ignore into journalissuearticles values(\alpha;z);$ for the class $\mathcal{P}insert ignore into journalissuearticles values(\alpha);$, a new class $\mathcal{Q}insert ignore into journalissuearticles values(\beta);$ of functions $qinsert ignore into journalissuearticles values(z);$ is introduced. The object of the present paper is to discuss some interesting coefficient inequalities for $qinsert ignore into journalissuearticles values(z);$ in the class $\mathcal{Q}insert ignore into journalissuearticles values(\beta);$.
Keywords : Analytic function, Carath`eodory function, extremal function, coefficient inequality

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