Best Möbius Approximations of Convex and Concave Mappings

被引：0

作者：

Chuaqui, Martin ^{[1
]}

Osgood, Brad ^{[2
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Matemat, Santiago, Chile

[2] Stanford Univ, Elect Engn, Palo Alto, CA 94025 USA

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2023年 / 25卷 / 1期

关键词：

Best Mobius approximation; Convex mappings; Concave mappings; Polygons; Blaschke product;

D O I：

10.1007/s40315-023-00517-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the best Mobius approximations (BMA) to convex and concave conformal mappings of the disk, including the special case of mappings onto convex polygons. The crucial factor is the location of the poles of the BMAs. Finer details are possible in the case of polygons through special properties of Blaschke products and the prevertices of the mapping function.

引用

页码：139 / 149

页数：11

共 50 条

[21] On generic convergence of successive approximations of mappings with convex and compact point images
Christian Bargetz
Emir Medjic
Katriin Pirk
Monatshefte für Mathematik, 2023, 202 : 659 - 683
[22] ON (k, h; m) -CONVEX MAPPINGS AND APPLICATIONS
Niezgoda, Marek
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2014, 17 (02): : 665 - 678
[23] A quasiconformal analog of Carathéodory’s criterion for the Möbius property of mappings
V. V. Aseev
Siberian Mathematical Journal, 2014, 55 : 1 - 6
[24] Common fixed points and best approximations in locally convex spaces
Saleh Abdullah Al-Mezel
Fixed Point Theory and Applications, 2011
[25] ON BEST RATIONAL APPROXIMATIONS OF CONVEX FUNCTIONS AND FUNCTIONS WITH FINITE VARIATION
BULANOV, AP
DOKLADY AKADEMII NAUK SSSR, 1970, 190 (01): : 13 - &
[26] Best approximations of convex compact sets by balls in the Hausdorff metric
Sosov, EN
MATHEMATICAL NOTES, 2004, 76 (1-2) : 209 - 218
[27] Best Approximations of Convex Compact Sets by Balls in the Hausdorff Metric
E. N. Sosov
Mathematical Notes, 2004, 76 : 209 - 218
[28] SOME ALGORITHMS FOR COMPUTING BEST APPROXIMATIONS FROM CONVEX CONES
DEUTSCH, F
MCCABE, JH
PHILLIPS, GM
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1975, 12 (03) : 390 - 403
[29] Common fixed points and best approximations in locally convex spaces
Al-Mezel, Saleh Abdullah
FIXED POINT THEORY AND APPLICATIONS, 2011,
[30] Disjointness of the Möbius Transformation and Möbius Function
El Houcein El Abdalaoui
Igor E. Shparlinski
Research in the Mathematical Sciences, 2019, 6

← 1 2 3 4 5 →