On a Multi-Point Schwarz-Pick Lemma

被引：7

作者：

Cho, Kyung Hyun ^{[1
]}

Kim, Seong-A ^{[2
]}

Sugawa, Toshiyuki ^{[3
]}

机构：

[1] Pohang Univ Sci & Technol, Dept Phys, Pohang 790784, Kyungbuk, South Korea

[2] Dongguk Univ, Dept Math Educ, Gyeongju 780714, Kyungbuk, South Korea

[3] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, Sendai, Miyagi 9808579, Japan

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2012年 / 12卷 / 02期

关键词：

Schwarz-Pick Lemma; Schur algorithm; Nevanlinna-Pick interpolation; Peschl's invariant derivative; Dieudonne's Lemma; INEQUALITY;

D O I：

10.1007/BF03321839

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the multi-point Schwarz-Pick Lemma and its associate functions due to Beardon-Minda and Baribeau-Rivard-Wegert. Basic properties of the associate functions are summarized. Then we observe that special cases of the multi-point Schwarz-Pick Lemma give the Schur's continued fraction algorithm and several inequalities for bounded analytic functions on the unit disk.

引用

页码：483 / 499

页数：17

共 18 条

[1] Ahlfors Lars V., 1973, Conformal Invariants: Topics in Geometric Function Theory
[2] [Anonymous], 1952, CONFORMAL MAPPINGS
[3] [Anonymous], 1948, ANAL THEORY CONTINUE
[4] Baribeau L., 2009, COMPUT METH FUNCT TH, V9, P391
[5] Beardon A. F., 2008, COMPUT METH FUNCT TH, V8, P409
[6] A multi-point Schwarz-Pick Lemma
Beardon, AF
Minda, D
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 2004, 92 (1): : 81 - 104
[7] A STRENGTHENING OF THE SCHWARZ-PICK INEQUALITY
BEARDON, AF
CARNE, TK
[J]. AMERICAN MATHEMATICAL MONTHLY, 1992, 99 (03) : 216 - 217
[8] Duren P. L., 1983, Univalent Functions
[9] Kaptanoglu HT, 2002, MICH MATH J, V50, P649
[10] Invariant differential operators associated with a conformal metric
Kim, Seong-A
Sugawa, Toshiyuki
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2007, 55 (02) : 459 - 479

← 1 2 →