Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

Let B be the unit ball in Cn with respect to an arbitrary norm and let f (z, t) be a g-Loewner chain such that e −tf (z, t)−z has a zero of order k +1 at z = 0. In this paper, we obtain growth and covering theorems for f (·, 0). Moreover, we consider coefficient bounds and examples of mappings in S0 g,k+1(B).  2005 Elsevier Inc. All rights reserved.