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

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.