Convexity Properties of Holomorphic Mappings in Cⁿ

Authors

Kevin A. Roper, Cedarville UniversityFollow
T. J. Suffridge

Document Type

Article

Publication Date

5-1999

Journal Title

Transactions of the American Mathematical Society

Volume

351

Issue

5

First Page

1803

Last Page

1833

Abstract

Not many convex mappings on the unit ball in Cⁿ for n > 1 are known. We introduce two families of mappings, which we believe are actually identical, that both contain the convex mappings. These families which we have named the "Quasi-Convex Mappings, Types A and B" seem to be natural generalizations of the convex mappings in the plane. It is much easier to check whether a function is in one of these classes than to check for convexity. We show that the upper and lower bounds on the growth rate of such mappings is the same as for the convex mappings.

Recommended Citation

Roper, Kevin A. and Suffridge, T. J., "Convexity Properties of Holomorphic Mappings in Cⁿ" (1999). Science and Mathematics Faculty Publications. 202.
https://digitalcommons.cedarville.edu/science_and_mathematics_publications/202