Publisher : Korea Society of Mathematical Education
DOI : 10.7468/jksmeb.2015.22.2.169
Title & Authors
CARATHÉODORY'S INEQUALITY ON THE BOUNDARY NAFI ORNEK, BULENT;
In this paper, a boundary version of Carathéodory’s inequality is investigated. Also, new inequalities of the Carathéodory’s inequality at boundary are obtained and the sharpness of these inequalities is proved.
Schwarz lemma on the boundary;Carathéodory’s inequality;Angular limit and derivative;Julia-Wolff-Lemma.;
H.P. Boas: Julius and Julia: Mastering the Art of the Schwarz lemma. Amer. Math. Monthly 117 (2010), 770-785.
V.N. Dubinin: The Schwarz inequality on the boundary for functions regular in the disc. J. Math. Sci. 122 (2004), no. 6, 3623-3629.
G.M. Golusin: Geometric Theory of Functions of Complex Variable [in Russian], 2nd edn., Moscow 1966.
M. Jeong: The Schwarz lemma and its applications at a boundary point. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 21 (2014), no. 3, 275-284.
M. Jeong: The Schwarz lemma and boundary fixed points. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 18 (2011), no. 3, 219-227.
D.M. Burns & S.G. Krantz: Rigidity of holomorphic mappings and a new Schwarz Lemma at the boundary. J. Amer. Math. Soc. 7 (1994), 661-676.
G. Kresin & V. Maz’ya: Sharp real-part theorems. A unified approach. Translated from the Russian and edited by T. Shaposhnikova. Lecture Notes in Mathematics, 1903. Springer, Berlin, 2007.
R. Osserman: A sharp Schwarz inequality on the boundary. Proc. Amer. Math. Soc. 128 (2000), 3513-3517.
T. Aliyev Azeroğlu & B.N. Örnek: A refined Schwarz inequality on the boundary. Complex Variables and Elliptic Equations 58 (2013), no. 4, 571-577.
B. N. Örnek: Sharpened forms of the Schwarz lemma on the boundary. Bull. Korean Math. Soc. 50 (2013), no. 6, 2053-2059.
Ch. Pommerenke: Boundary Behaviour of Conformal Maps. Springer-Verlag, Berlin, 1992.