Bohr-Rogosinski phenomenon for $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$

TL;DR

This paper investigates the Bohr-Rogosinski phenomenon within the classes of Ma-Minda starlike and convex functions, extending understanding of radius problems in geometric function theory.

Contribution

It introduces the study of the Bohr-Rogosinski radius for subclasses of analytic functions defined via subordination in Ma-Minda classes, providing new insights and applications.

Findings

Established Bohr-Rogosinski radius bounds for $ ext{S}^*( ext{ extpsi})$ and $ ext{C}( ext{ extpsi})$.

Extended the concept of Bohr's phenomenon to Rogosinski radius in these classes.

Applied results to specific subclasses of univalent functions.

Abstract

In Geometric function theory, occasionally attempts have been made to solve a particular problem for the Ma-Minda classes, $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ of univalent starlike and convex functions, respectively. Recently, a popular radius problem generally known as Bohr's phenomenon has been studied in various settings, however little is known about Rogosinski radius. In this article, for a fixed $f\in \mathcal{S}^*(\psi)$ or $\mathcal{C}(\psi),$ the class of analytic subordinants $S_{f}(\psi):= \{g : g\prec f \} $ is studied for the Bohr-Rogosinski phenomenon in a general setting. It's applications to the classes $\mathcal{S}^*(\psi)$ and $\mathcal{C}(\psi)$ are also shown.