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A SHARP SCHWARZ LEMMA AT THE BOUNDARY
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  • Journal title : The Pure and Applied Mathematics
  • Volume 22, Issue 3,  2015, pp.263-273
  • Publisher : Korea Society of Mathematical Education
  • DOI : 10.7468/jksmeb.2015.22.3.263
 Title & Authors
A SHARP SCHWARZ LEMMA AT THE BOUNDARY
AKYEL, TUGBA; ORNEK, NAFI;
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 Abstract
In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z)
 Keywords
Schwarz lemma on the boundary;angular limit and derivative;Julia-Wolff-Lemma;holomorphic function;
 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.
D. Chelst: A generalized Schwarz lemma at the boundary. Proc. Amer. Math. Soc. 129 (2001), no. 11, 3275-3278. crossref(new window)

3.
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)

4.
______: Bounded holomorphic functions covering no concentric circles. Zap. Nauchn. Sem. POMI 429 (2015), 34-43.

5.
G.M. Golusin: Geometric Theory of Functions of Complex Variable [in Russian]. 2nd edn., Moscow 1966.

6.
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.

7.
______: The Schwarz lemma and boundary fixed points. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 18 (2011), no. 3, 219-227.

8.
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)

9.
X. Tang & T. Liu: The Schwarz Lemma at the Boundary of the Egg Domain Bp1,p2 in ℂn. Canad. Math. Bull. 58 (2015), no. 2, 381-392. crossref(new window)

10.
X. Tang, T. Liu & J. Lu: Schwarz lemma at the boundary of the unit polydisk in ℂn. Sci. China Math. 58 (2015), 1-14.

11.
R. Osserman: A sharp Schwarz inequality on the boundary. Proc. Amer. Math. Soc. 128 (2000), 3513–3517. crossref(new window)

12.
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)

13.
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)

14.
Ch. Pommerenke: Boundary Behaviour of Conformal Maps. Springer-Verlag, Berlin, 1992.