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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The object of the present paper is to discuss some interesting coefficient inequalities for $q(z)$ in the class $\mathcal{Q}(\beta)$.
📌 3 Key Takeaways
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Objective & Hypothesis: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 $\mathbb{U}$.
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Key Findings & Data: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.
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Conclusion & Impact:The object of the present paper is to discuss some interesting coefficient inequalities for $q(z)$ in the class $\mathcal{Q}(\beta)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Analytic function · Carath\'eodory function · extremal function
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 $\mathcal{Q}(\beta)$.
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Cite This Article
Owa, S. (2017). AN APPLICATION OF CARATHEODORY FUNCTIONS. Konuralp Journal of Mathematics, Volume: 5 Issue: 2. https://ajindex.com/articles/1521813