Asymptotic estimates for the coefficients of bounded univalent functions

被引：0

作者：

Prokhorov, D. V. ^{[1
]}

Nikulin, A. A. ^{[1
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Saratov, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2006年 / 47卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

univalent function; bounded function; coefficient estimate; Lowner equation; asymptotic estimate;

D O I：

10.1007/s11202-006-0103-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the class of univalent bounded normalized holomorphic functions in the unit disk, we give an asymptotic estimate for the coefficients when the uniform norm of the modulus of the function tends to infinity.

引用

页码：924 / 933

页数：10

共 18 条

[1]

Aleksandrov I. A., 1976, PARAMETRIC EXTENSION

[2]

Bazilevich I. E., 1957, MAT SBORNIK, V43, P409

[3] A COEFFICIENT PROBLEM OF BOMBIERI CONCERNING UNIVALENT-FUNCTIONS [J].

BSHOUTY, D .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 91 (03) :383-388

[4]

de Branges L, 1984, E584 LOMI

[5] A PROOF OF THE BIEBERBACH CONJECTURE [J].

DEBRANGES, L .

ACTA MATHEMATICA, 1985, 154 (1-2) :137-152

[6] Analysis on simple conformable illustrations of unit circles I [J].

Lowner, K .

MATHEMATISCHE ANNALEN, 1923, 89 :103-121

[7]

Pick G., 1917, S B KAISERL AKAD WIS, V126, P247

[8]

Pontryagin L. S., 1969, MATH THEORY OPTIMAL

[9]

Prokhorov D., 2005, GEORGIAN MATH J, V12, P743, DOI [DOI 10.1515/GMJ.2005.743, 10.1515/GMJ.2005.743]

[10]

Prokhorov D.V., 2002, Handbook of Complex Analysis: Geometric Function Theory, V1, P207

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