Vol. 33, No. 1, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
The principle of subordination applied to functions of several variables

Ted Joe Suffridge

Vol. 33 (1970), No. 1, 241–248
Abstract

In this paper we consider univalent maps of domains in Cn(n 2). Let P be a polydisk in Cn. We find necessary and sufficient conditions that a function f : P−→ Cn be univalent and map the polydisk P onto a starlike or a convex domain. We also consider maps from

Dp = {z : |z|p < 1} ⊂ Cn

(1)

                       n
∑    p 11p
|z|p = |(z1,z2,⋅⋅⋅ ,zn)|p = [ |zj|]  ,p ≧ 1
j=1

into Cn and give necessary and sufficient conditions that such a map have starlike or convex image.

Mathematical Subject Classification
Primary: 32.60
Milestones
Received: 19 May 1969
Published: 1 April 1970
Authors
Ted Joe Suffridge