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ISSN : 1226-0657

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Vol.23 No.1

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AN IMPROVED LOWER BOUND FOR 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
2016, v.23 no.1, pp.61-72
https://doi.org/10.7468/jksmeb.2016.23.1.61
ORNEK, BULENT NAFI
AKYEL, TUGBA
ORNEK,, B. N. , & AKYEL,, T. (2016). AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(1), 61-72, https://doi.org/10.7468/jksmeb.2016.23.1.61

Abstract

In this paper, a boundary version of the Schwarz lemma for the holom- rophic function satisfying f(a) = b, |a| < 1, b ∈ ℂ and ℜf(z) > α, 0 ≤ α < |b| for |z| < 1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c) = a. The sharpness of these inequalities is also proved.

keywords
angular derivative, holomorphic function, Schwarz lemma on the boundary

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