Let $\mathcal{S}^*_{Ne}$ be the collection of all analytic functions $f(z)$ defined on the open unit disk $\mathbb{D}$ and satisfying the normalizations $f(0)=f'(0)-1=0$ such that the quantity $zf'(z)/f(z)$ assumes values from the range of the function $\varphi_{\scriptscriptstyle{Ne}}(z):=1+z-z^3/3\,,z\in\mathbb{D}$, which is the interior of the nephroid given by \begin{align*} \left((u-1)^2+v^2-\frac{4}{9}\right)^3-\frac{4 v^2}{3}=0. \end{align*} In this work, we find sharp $\mathcal{S}^*_{Ne}$-radii for several geometrically defined function classes introduced in the recent past. In particular, $\mathcal{S}^*_{Ne}$-radius for the starlike class $\mathcal{S}^*$ is found to be $1/4$. Moreover, radii problems related to the families defined in terms of ratio of functions are also discussed. Sharpness of certain radii estimates are illustrated graphically.

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与肾样结构域相关的功能的半径问题

令 $\mathcal{S}^*_{Ne}$ 是定义在开放单元盘 $\mathbb{D}$ 上并满足归一化的所有解析函数 $f(z)$ 的集合 $f(0)= f'(0)-1=0$ 使得数量 $zf'(z)/f(z)$ 假定值来自函数 $\varphi_{\scriptscriptstyle{Ne}}(z):=1 +zz^3/3\,,z\in\mathbb{D}$，这是由 \begin{align*} \left((u-1)^2+v^2-\ frac{4}{9}\right)^3-\frac{4 v^2}{3}=0。\end{align*} 在这项工作中，我们为最近引入的几个几何定义的函数类找到了尖锐的 $\mathcal{S}^*_{Ne}$-radii。特别是，发现类星类 $\mathcal{S}^*$ 的 $\mathcal{S}^*_{Ne}$-半径为 $1/4$。此外，还讨论了与以函数比定义的族相关的半径问题。