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

Abstract

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