We consider normalized analytic function f on the open unit disk for which either \(Ref(z)/g(z)>0\), \(|f(z) /g(z) - 1|<1\) or \(Re(1-z^2) f(z) /z>0\) for some analytic function g with \(Re(1-z^2) g(z) /z>0\). We have obtained the radii for these functions to belong to various subclasses of starlike functions. The subclasses considered include the classes of starlike functions of order \(\alpha \), lemniscate starlike functions and parabolic starlike functions.

中文翻译：

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类解析函数的星形半径

我们考虑开放单元磁盘上的归一化分析函数f，其中\（Ref（z）/ g（z）> 0 \），\（| f（z）/ g（z）-1 | <1 \）或\（Re（1-z ^ 2）f（z）/ z> 0 \）对于具有\（Re（1-z ^ 2）g（z）/ z> 0 \）的某些解析函数g。我们已经获得了这些函数属于星形函数的各种子类的半径。所考虑的子类包括\（\ alpha \）阶星形函数，lemniscate星形函数和抛物线星形函数的类。