22 research outputs found
On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable
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