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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.21 No.3

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THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT

THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2014, v.21 no.3, pp.219-227
https://doi.org/10.7468/jksmeb.2014.21.3.219
Jeong, Moonja (Department of Mathematics, The University of Suwon)
Jeong, Moonja. (2014). THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT. 한국수학교육학회지시리즈B:순수및응용수학, 21(3), 219-227, https://doi.org/10.7468/jksmeb.2014.21.3.219

Abstract

In this note we study the Schwarz lemma and inequalities for some holomorphic functions on the unit disc. Also, we obtain the inequality of the derivative of holomorphic maps at a boundary point of the unit disc and find a holomorphic map to satisfy the equality.

keywords
Schwarz lemma, boundary point, unit disc, holomorphic map

참고문헌

1.

H.P. Boas. (2010). Julius and Julia: Mastering the Art of the Schwarz Lemma. Amer. Math. Monthly, 117, 770-785. 10.4169/000298910X521643.

2.

R. Greene & S. Krantz. Function theory of one complex variable, Graduate studies on Mathematics Vol. 40.

3.

Jeong, Moon-Ja;. (2011). THE SCHWARZ LEMMA AND BOUNDARY FIXED POINTS. The Pure and Applied Mathematics, 18(3), 275-284. 10.7468/jksmeb.2011.18.3.275.

4.

Z. Nehari. Conformal Mapping.

5.

B. Ornek. (2013). Scharpened forms of the Schwarz lemma on the boundary. Bull. Korean Math. Soc., 50, 2053-2059. 10.4134/BKMS.2013.50.6.2053.

6.

R. Osserman. (2000). A Sharp Schwarz Inequality on the boundary. Proc. Amer. Math. Soc., 128, 3513-3517. 10.1090/S0002-9939-00-05463-0.

7.

H. Silverman. Complex Variables.

한국수학교육학회지시리즈B:순수및응용수학

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