Sharp inequalities of homogeneous expansions for quasi-convex mappings of type B and almost starlike mappings of order alpha

Abstract

In this paper, we first obtain several sharp inequalities of homogeneous expansion for both the subclass of all normalized biholomorphic quasi-convex mappings of type B and order alpha and the subclass of all normalized biholomorphic almost starlike mappings of order alpha defined on the unit ball $B$ of a complex Banach space X. Then, with these sharp inequalities, we derive the sharp estimates of the third and fourth homogeneous expansions for the above mappings defined on the unit polydisk $D^n$ in C(n).

arXiv comment23 pages, Submitted to AMC in August, 2014

References in corpus (1)

• Polynomial estimates and radius of analyticity on real Banach spaces