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

Abstract

In Geometric function theory, occasionally attempts have been made to solve a particular problem for the Ma-Minda classes, ${\mathcal{S}}^{\ast }(\psi )$ 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 $f\in {\mathcal{S}}^{\ast }(\psi )$ 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 ${\mathcal{S}}^{\ast }(\psi )$ and $\mathcal{C}(\psi )$ are also shown.