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Starlikeness for functions of a hypercomplex variable

Authors: Anna Gori and Fabio Vlacci
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 30G35, 30C45
Published electronically: August 23, 2016
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Abstract: In this paper we introduce new notions of starlikeness for a class of functions of a hypercomplex variable. We then obtain equivalent formulations for starlikeness which resemble the analogous ones in the holomorphic case such as Nevanlinna's criterion. Furthermore we give a characterization of algebraic starlikeness in terms of non-vanishing of a suitable analog of the Hadamard product.

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Anna Gori
Affiliation: Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy

Fabio Vlacci
Affiliation: Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze Viale Morgagni 67/A, 50134 Firenze, Italy

Keywords: Regular functions of one quaternionic variable, univalent functions, starlikeness and starlike or star--shaped function, convexity and convex--function
Received by editor(s): July 27, 2015
Received by editor(s) in revised form: March 3, 2016, April 7, 2016, and April 20, 2016
Published electronically: August 23, 2016
Additional Notes: This work was partially supported by Progetto MIUR di Rilevante Interesse Nazionale PRIN 2010-11 Varietà reali e complesse: geometria, topologia e analisi armonica. The research that led to the present paper was partially supported by a grant of the group GNSAGA of Istituto Nazionale di Alta Matematica “F: Severi”.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2016 American Mathematical Society