Coefficient bounds for biholomorphic mappings which have a parametric representation

Let B be the unit ball in C n with respect to an arbitrary norm ‖ ⋅ ‖ and let f ( z , t ) be a g-Loewner chain such that z = 0 is a zero of order k + 1 of e − t f ( z , t ) − z for each t ⩾ 0 . In this paper, the authors obtain coefficient bounds of mappings in S g , k + 1 0 ( B ) . These results generalize the related works of Hamada, Honda and Kohr.