关于从属族的极值问题

On Extremal Problems of Subordination Classes

设 U={z:|z|<1},H={f:f在U内解析},B={f∈H:f(U)=U},B_0={f∈B:f(0)=0},S(f)={g∈H:g f}。α_1…,α_m是U内不同的复数。给定正整数K_1,K_2,…

The extremal points of variability regions B_n(α_1,...,α_m) and S_n(α_1,...,α_m) are discussed in the first part ofthis paper. Frechet differentiable functioal on S(f) is also discussed. Inthe second part the extreme__points of {f∈Hlog(1+H): ‖f‖=1} are discussed, and a sufficient condition for f∈ES(F) is given, where F∈Hlog(1+H).