Sharp radius of concavity for certain classes of analytic functions

Molla Basir Ahamed, Rajesh Hossain
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Abstract

Let $\mathcal{A}$ be the class of all analytic functions $f$ defined on the open unit disk $\mathbb{D}$ with the normalization $f(0)=0=f^{\prime}(0)-1$. This paper examines the radius of concavity for various subclasses of $\mathcal{A}$, namely $\mathcal{S}_0^{(n)}$, $\mathcal{K(\alpha,\beta)}$, $\mathcal{\tilde{S^*}(\beta)}$, and $\mathcal{S}^*(\alpha)$. It also presents results for various classes of analytic functions on the unit disk. All the radii are best possible.
某类解析函数的锐凹半径
设 $\mathcal{A}$ 是定义在开放单位盘 $\mathbb{D}$ 上的所有解析函数 $f$ 的类,其归一化为 $f(0)=0=f^\{prime}(0)-1$。本文研究了$\mathcal{A}$的各种子类,即$\mathcal{S}_0^{(n)}$、$\mathcal{K(\alpha,\beta)}$、$\mathcal{tilde{S^*}(\beta)}$和$\mathcal{S}^*(\alpha)$的凹半径。它还给出了单位盘上各类解析函数的结果。所有的adii都是最可能的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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