Coefficient Inequalities for Biholomorphic Mappings on the Unit Ball of a Complex Banach Space

In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. Hamada, G. Kohr and M. Kohr. We obtain the Fekete–Szegö inequalities using the norm under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. In the second part of this paper, we give the estimation of the difference of the moduli of successive coefficients for the first elements of g-Loewner chains on the unit disc. We also give the estimation of the difference of the moduli of successive coefficients for the first elements F of g-Loewner chains on the unit ball of a complex Banach space under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F.