ON SHARP INEQUALITIES OF HOMOGENEOUS EXPANSIONS FOR STARLIKE MAPPINGS OF ORDER $\alpha$ IN SEVERAL COMPLEX VARIABLES

Abstract

In this paper, we establish sharp inequalities of homogeneous expansions for starlike mappings and starlike mappings of order $\alpha$ defined on the unit ball of Banach complex spaces. As corollaries, we also obtain the sharp estimates of the third homogeneous expansions for the above mappings defined on the unit polydisk in $\mathbb{C}^n$ with some restricted conditions.