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CARATHÉODORY'S INEQUALITY ON THE BOUNDARY
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  • Journal title : The Pure and Applied Mathematics
  • Volume 22, Issue 2,  2015, pp.169-178
  • 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;
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 Abstract
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.
 Keywords
Schwarz lemma on the boundary;Carathéodory’s inequality;Angular limit and derivative;Julia-Wolff-Lemma.;
 Language
English
 Cited by
 References
1.
H.P. Boas: Julius and Julia: Mastering the Art of the Schwarz lemma. Amer. Math. Monthly 117 (2010), 770-785. crossref(new window)

2.
V.N. Dubinin: The Schwarz inequality on the boundary for functions regular in the disc. J. Math. Sci. 122 (2004), no. 6, 3623-3629. crossref(new window)

3.
G.M. Golusin: Geometric Theory of Functions of Complex Variable [in Russian], 2nd edn., Moscow 1966.

4.
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.

5.
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.

6.
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. crossref(new window)

7.
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.

8.
R. Osserman: A sharp Schwarz inequality on the boundary. Proc. Amer. Math. Soc. 128 (2000), 3513-3517. crossref(new window)

9.
T. Aliyev Azeroğlu & B.N. Örnek: A refined Schwarz inequality on the boundary. Complex Variables and Elliptic Equations 58 (2013), no. 4, 571-577. crossref(new window)

10.
B. N. Örnek: Sharpened forms of the Schwarz lemma on the boundary. Bull. Korean Math. Soc. 50 (2013), no. 6, 2053-2059. crossref(new window)

11.
Ch. Pommerenke: Boundary Behaviour of Conformal Maps. Springer-Verlag, Berlin, 1992.