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

ISSN : 1226-0657

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Vol.22 No.3

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A SHARP SCHWARZ LEMMA AT THE BOUNDARY

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.3, pp.263-273
https://doi.org/10.7468/jksmeb.2015.22.3.263
AKYEL, TUGBA
ORNEK, NAFI
AKYEL,, T. , & ORNEK,, N. (2015). A SHARP SCHWARZ LEMMA AT THE BOUNDARY. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(3), 263-273, https://doi.org/10.7468/jksmeb.2015.22.3.263

Abstract

In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z) = a + c<sub>p</sub>z<sup>p</sup> + c<sub>p</sub>+<sub>1</sub>z<sup>p+1</sup> + ... defined in the unit disc satisfying |f(z) &#x2212; 1| &#x3C; 1, where 0 &#x3C; a &#x3C; 2, we estimate a module of angular derivative at the boundary point b, f(b) = 2, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

keywords
Schwarz lemma on the boundary, angular limit and derivative, Julia-Wolff-Lemma, holomorphic function

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