On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable
Complex Variables
2014-10-13 v1
Abstract
The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of results, among which an Area-type Theorem, Rogosinski inequality, and a Bieberbach-de Branges Theorem for a subclass of slice regular functions. We also discuss some geometric and algebraic interpretations of our results in terms of maps from to itself. As a tool for subordination we define a suitable notion of composition of slice regular functions which is of independent interest.
Cite
@article{arxiv.1410.2623,
title = {On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable},
author = {Sorin G. Gal and J. Oscar González-Cervantes and Irene Sabadini},
journal= {arXiv preprint arXiv:1410.2623},
year = {2014}
}