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A SHARP CARATHÉODORY`S INEQUALITY ON THE BOUNDARY
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 Title & Authors
A SHARP CARATHÉODORY`S INEQUALITY ON THE BOUNDARY
Ornek, Bulent Nafi;
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 Abstract
In this paper, a generalized boundary version of inequality for holomorphic function satisfying $f(z)
 Keywords
holomorphic function;Schwarz lemma on the boundary; inequality;
 Language
English
 Cited by
 References
1.
T. Akyel and B. N. Ornek, A sharp Schwarz lemma at the boundary, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 22 (2015), no. 3, 263-273.

2.
T. Aliyev Azeroglu and B. N. Ornek, A refined Schwarz inequality on the boundary, Complex Var. Elliptic Equ. 58 (2013), no. 4, 571-577. crossref(new window)

3.
H. P. Boas, Julius and Julia: Mastering the art of the Schwarz lemma, Amer. Math. Monthly 117 (2010), no. 9, 770-785. crossref(new window)

4.
D. M. Burns and S. G. Krantz, Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary, J. Amer. Math. Soc. 7 (1994), no. 3, 661-676. crossref(new window)

5.
D. Chelst, A generalized Schwarz lemma at the boundary, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3275-3278. crossref(new window)

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

7.
G. M. Golusin, Geometric Theory of Functions of Complex Variable, 2nd edn., Moscow 1966.

8.
M. Jeong, The Schwarz lemma and boundary fixed points, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 18 (2011), no. 3, 275-284.

9.
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, 219-227.

10.
G. Kresin and 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.

11.
M. Mateljevic, Ahlfors-Schwarz lemma and curvature, Kragujevac J. Math. 25 (2003), 155-164.

12.
M. Mateljevic, Distortion of harmonic functions and harmonic quasiconformal quasi-isometry, Rev. Roumaine Math. Pures Appl. 51 (2006), no. 5-6, 711-722.

13.
M. Mateljevic, The lower bound for the modulus of the derivatives and Jacobian of harmonic injective mappings, Filomat 29 (2015), no. 2, 221-244. crossref(new window)

14.
M. Mateljevic, Note on rigidity of holomorphic mappings & Schwarz and Jack lemma, (in preparation) ResearchGate.

15.
B. N. Ornek, Sharpened forms of the Schwarz lemma on the boundary, Bull. Korean Math. Soc. 50 (2013), no. 6, 2053-2059. crossref(new window)

16.
B. N. Ornek, Caratheodory's inequality on the boundary, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math. 22 (2015), no. 2, 169-178.

17.
R. Osserman, A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc. 128 (2000), no. 12, 3513-3517. crossref(new window)

18.
Ch. Pommerenke, Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.

19.
X. Tang, T. Liu, and J. Lu, Schwarz lemma at the boundary of the unit polydisk in $\mathbb{C}^n$, Sci. China Math. 58 (2015), no. 8, 1639-1652. crossref(new window)