Extension of convex mappings of order α of the unit disk in C to convex mappings of the unit ball in Cn

For a convex mapping f of order alpha is an element of [0, 1) of the unit disk in the complex plane C, we consider conditions on the parameter beta is an element of [0, 1/2] so that the mapping F(z) = (f(z(1)), [f'(z(1))](beta)(z) over cap), (z) over cap = (z(2),...,z(n)), is a convex mapping of the Euclidean unit ball in C-n. (C) 2009 Elsevier Inc. All rights reserved.