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arXiv · 2201.05811

On a subfamily of starlike functions related to Hyperbolic Cosine function

Mridula Mundalia·S. Sivaprasad Kumar
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Abstract

We introduce and study a new Ma-Minda subclass of starlike functions $\mathcal{S}^*_{\varrho},$ defined as $$\mathcal{S}^{*}_{\varrho}:=\left\{f\in\mathcal{A}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho(z), z\in\mathbb{D} \right\},$$ associated with an analytic univalent function $\cosh \sqrt{z},$ where we choose the branch of the square root function so that $\cosh\sqrt{z}=1+z/2!+z^{2}/{4!}+\cdots.$ We establish certain inclusion relations for $\mathcal{S}^{*}_{\varrho}$ and deduce sharp $\mathcal{S}^{*}_{\varrho}-$radii for certain subclasses of analytic functions.

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Mridula Mundalia, S. Sivaprasad Kumar. 2022-01-15. On a subfamily of starlike functions related to Hyperbolic Cosine function. https://arxiv.org/abs/2201.05811

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