We investigate some geometric properties of the class $\mathcal{Q}_n(A,B,\alpha)$ which is defined by the second-order differential subordination and find the sharp lower bound on $|z|=r<1$ for the following functional: $$\mathrm{Re}\left\{(1-\alpha)z^{1-p}f'(z) +\frac{\alpha}{p-1}z^{2-p}f''(z)\right\}$$ over the class $\mathcal{Q}_n(A,B,0)$.

中文翻译：

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一类与二阶微分从属相关的多价解析函数的几何性质

我们研究了类$ \ mathcal {Q} _n（A，B，\ alpha）$的一些几何性质，该类由二阶微分从属定义，并找到$ | z | = r <1 $的尖锐下界以下功能：$$ \ mathrm {Re} \ left \ {（1- \ alpha）z ^ {1-p} f'（z）+ \ frac {\ alpha} {p-1} z ^ {2 -p} f''（z）\ right \} $$超过类别$ \ mathcal {Q} _n（A，B，0）$。