A generalized Bohr-Rogosinski phenomenon

TL;DR

This paper extends the Bohr-Rogosinski phenomenon to various classes of starlike and convex functions, exploring new generalizations and their connections to existing results with illustrative examples.

Contribution

It introduces a generalized Bohr-Rogosinski sum for Ma-Minda classes and related subclasses, broadening the scope of the phenomenon in geometric function theory.

Findings

Generalized Bohr-Rogosinski sums for Ma-Minda classes

Connections established with known results

Illustrative examples demonstrating the generalizations

Abstract

In this paper, we generalize the Bohr-Rogosinski sum for the Ma-Minda classes of starlike and convex functions. Also the phenomenon is studied for the classes of starlike functions with respect to symmetric points and conjugate points along with their convex cases. Further, the connection between the derived results and the known ones are established with the suitable examples.