【摘 要】
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In this article,first,a sufficient condition for a starlike mapping of order α f(x) defined on the unit ball in a complex Banach space is given. Second,the sha
【机 构】
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School of Mathematics and Computation Science,Department of Mathematics
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In this article,first,a sufficient condition for a starlike mapping of order α f(x) defined on the unit ball in a complex Banach space is given. Second,the sharp estimate of the third homogeneous expansion for f is established as well,where f(z) =(f1(z),f2(z),…,fn(z))' is a starlike mapping of order α or a normalized biholomorphic starlike mapping defined on the unit polydisk in Cn,and D2fk(0)(z2)/2 =zk(nΣl=1 aklzl),k =1,2,…,n,here,akl =1/2!(6)2fk(0)/(6)zk(6)zl,k,l==1,2,…,n.Our result states that the Bieberbach conjecture in several complex variables (the case of the third homogeneous expansion for starlike mappings of order α and biholomorphic starlike mappings) is partly proved.
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