On certain Generalizations of ${\mathcal{S}}^{\ast }(\psi )$: II

Abstract

In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes ${\mathcal{S}}^{\ast }(\psi )$ 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 $f\in {\mathcal{S}}^{\ast }(\psi ).$ The results are improvements and generalizations of several well known results.

second half of the main results are from arXiv:2007.06069