On certain analytic functions of bounded boundary rotation

TL;DR

This paper introduces classes of analytic functions with bounded boundary rotation, originating from Caratheodory functions, and studies their properties within the unit disk.

Contribution

It defines new classes of functions with bounded boundary rotation based on Caratheodory functions and analyzes their univalence and boundary behavior.

Findings

Characterization of functions with boundary rotation bounded by kπ

Establishment of properties of these functions within the unit disk

Extension of classical results to new function classes

Abstract

In this paper we introduce certain analytic functions of boundary rotation bounded by $k\pi$ which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk $E=\{z\in \mathbb{C}\colon |z|<1\}$, which are also of bounded boundary rotation.