THE SCHWARZ LEMMA AND BOUNDARY FIXED POINTS

被引:20
作者
Jeong, Moonja [1 ]
机构
[1] Univ Suwon, Dept Math, Gyeonggi Do 445743, South Korea
来源
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS | 2011年 / 18卷 / 03期
关键词
Schwarz lemma; boundary fixed point; unit disc; holomorphic map;
D O I
10.7468/jksmeb.2011.18.3.275
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this note we study the Schwarz lemma and its various versions. We find a condition for a holomorphic map to have fixed points only on the boundary of the unit disc and compare its derivatives at fixed points to get some relations among them.
引用
收藏
页码:275 / 284
页数:10
相关论文
共 15 条
[1]   Julius and Julia: Mastering the Art of the Schwarz Lemma [J].
Boas, Harold P. .
AMERICAN MATHEMATICAL MONTHLY, 2010, 117 (09) :770-785
[2]   Covering properties of meromorphic functions, negative curvature and spherical geometry [J].
Bonk, M ;
Eremenko, A .
ANNALS OF MATHEMATICS, 2000, 152 (02) :551-592
[3]  
Burns DM., 1994, J AM MATH SOC, V7, P661, DOI [DOI 10.1090/S0894-0347-1994-1242454-2, 10.1090/S0894-0347-1994-1242454-2]
[4]  
Caratheodory C., 1954, THEORY FUNCTIONS COM, VII
[5]  
Cases J., 2008, SIAM NEWS, V41
[6]   FUNCTIONS STARLIKE AND CONVEX OF ORDER ALPHA [J].
JACK, IS .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1971, 3 (APR) :469-&
[7]  
Julia G, 1920, ACTA MATH-DJURSHOLM, V42, P349, DOI 10.1007/BF02404416
[8]   Sharpened versions of the Schwarz Lemma [J].
Mercer, PR .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 205 (02) :508-511
[9]  
Nehari Z, 1952, CONFORMAL MAPPING
[10]   A sharp Schwarz inequality on the boundary [J].
Osserman, R .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (12) :3513-3517