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

TL;DR

This paper extends the theory of Ma-Minda classes of starlike and convex functions by establishing radius results, convolution conditions, and the Bohr radius, thereby generalizing and improving existing results in geometric function theory.

Contribution

It provides new radius results, convolution-based sufficient conditions, and the Bohr radius for generalized classes of analytic functions, enhancing prior work in the field.

Findings

Established new radius results for Ma-Minda classes.

Derived sufficient convolution conditions for these classes.

Calculated the Bohr radius for a class of subordinate functions.

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.