Bohr-Rogosinski type inequalities for concave univalent functions

TL;DR

This paper extends Bohr-Rogosinski inequalities to concave univalent functions, analyzing their properties and establishing sharp results for functions mapping the unit disk to concave domains.

Contribution

It generalizes classical inequalities to a new class of univalent functions with sharp bounds, enriching the theory of geometric function analysis.

Findings

Established generalized Bohr-Rogosinski inequalities for concave univalent functions.

Proved the sharpness of all derived inequalities.

Extended the Bohr-Rogosinski phenomenon to concave domains.

Abstract

In this paper, we generalize and investigate Bohr-Rogosinski's inequalities and the Bohr-Rogosinski phenomenon for the subfamilies of univalent (i.e., one-to-one) functions defined on unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1 \}$ which maps to the concave domain, i.e., the domain whose complement is a convex set. All the results are proved to be sharp.