2015/11/22 by Ming-Sheng Liu, Liu, Ming-Sheng, Fen Wu +3
Mathematics · #32A30 #32H02 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32A30 #msc:32H02
paper · pdf · doi:10.48550/arxiv.1511.06949
23 pages, Submitted to AMC in August, 2014
arxiv created 2015/11/22 · arxiv updated 2015/11/24
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 Dn in C(n).