The sum of coefficients of bounded univalent functions

被引：0

作者：

Prokhorov, DV ^{[1
]}

机构：

[1] NG CHERNYSHEVSKII SARATOV STATE UNIV,SARATOV,RUSSIA

来源：

MATHEMATICAL NOTES | 1997年 / 61卷 / 5-6期

关键词：

holomorphic functions; Pick functions; Koebe functions; maximal value problem;

D O I：

10.1007/BF02355082

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We solve the maximal value problem for the functional Re Sigma(j=1)(m)a(kj) in the class of functions f(z) = z + a(2)z(2) + ... that are holomorphic and univalent in the unit disk and satisfy the inequality \f(z)\ < M. We prove that the Pick functions are extremal for this problem for sufficiently large M whenever the set of indices k(1),..., k(m) contains an even number.

引用

页码：609 / 613

页数：5

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