On certain Generalizations of $\mathcal{S}^*(ψ)$: II (2106.04962v1)

Abstract: In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of starlike and convex analytic functions. We also obtain the Bohr radius for the class $ S_{f}(\psi):= {g(z)=\sum_{k=1}^{\infty}b_k z^k : g \prec f }$ of subordinants, where $f\in \mathcal{S}^*(\psi).$ The results are improvements and generalizations of several well known results.