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Radii problems for Ma-Minda Starlikeness (2007.07816v2)

Published 15 Jul 2020 in math.CV

Abstract: For the standard Ma-Minda class $\mathcal{S}{*}(\psi)$ of univalent starlike functions, we derive $\mathcal{S}{*}(\psi)$-radii for some well-known special functions. In addition, we obtain the set of extremal functions for the classical problem $$\max_{f\in \mathcal{S}{*}(\psi)}{}\left|\Phi\left(\log{(f(z)/z)}\right)\right| \quad \text{or} \quad \max_{f\in \mathcal{S}{*}(\psi)}{}\Re\Phi\left(\log{(f(z)/z)}\right),$$ where $\Phi$ is a non-constant entire function. Moreover, we prove certain results on convolution and radius estimates for the case when $\psi(\mathbb{D})$ is starlike.

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