Coecient Inequality Of A Subclass Of Starlike Mappings In Complex Banach Space And The Bounded Starlike Circular Domain In C~n

This paper mainly studies coefficient inequalities for a subclass of starlike mappings in complex Banach space on the unit ball and on the bounded starlike circular domain in Cn,as well as the coefficient estimates annotation for certain subclasses of starlike.functions of complex order.This paper is composed with four chapters.In the first chapter,we briefly introduced Fekete-Szego inequality and coeffi?cient estimation research background and some definitions or notation used in this paper.In the second chapter,we introduced the several complex variables Fekete-Szeg o problem research background and definition,the corresponding problem for the subclass of strongly starlike mappings of order a defined on the unit ball in a complex Banach space,on the unit polydisk in Cn and the bounded starlike circular domain in Cn,respectively.In the third chapter,we introduced the p-valent function definition of quasi-subordination classes:and then calculate the function class Fekete-Szeg o inequality.In chapter fourwe reduce the conditions of the lemma in the coefficient esti-mates for subclasses of starlike function of complex order,thus,a conjecture was proposed.