Vol. 33, No. 1, 1970

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ISSN: 0030-8730
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