Some sufficient conditions for biholomorphic convex mappings on Bn p ✩

A few biholomorphic convex mappings on the unit ball in Cn for n>1 are known. In this paper, we shall prove some sufficient conditions for biholomorphic convex mappings on Reinhardt domain Bn p in Cn. Some results of Roper and Suffridge, Hamada and Kohr on Bn 2 are extended to Bn p. From these, we may construct some concrete biholomorphic convex mappings on Bn p.  2005 Elsevier Inc. All rights reserved.