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arXiv · 2008.06833

A Cardioid Domain and Starlike Functions

S. Sivaprasad Kumar·Kamaljeet Gangania
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Abstract

We introduce and study a class of starlike functions defined by \begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}: \frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$ maps the unit disk onto a cardioid domain. We find the radius of convexity of $\wp(z)$ and establish the inclusion relations between the class $ \mathscr{S}^*_\wp$ and some well-known classes. Further we derive sharp radius constants and coefficient related results for the class $ \mathscr{S}^*_\wp$.

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S. Sivaprasad Kumar, Kamaljeet Gangania. 2020-08-16. A Cardioid Domain and Starlike Functions. https://doi.org/10.1007/s13324-021-00483-7

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