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AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY

Bülent Nafi ÖRNEK|Tuğba AKYEL
한국수학교육학회|2016.02|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제23권 제1호|pp. 61-72

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참고문헌

키워드

holomorphic functionangular derivativeSchwarz lemma on the boundary.
주제분류수학

초록

In this paper, a boundary version of the Schwarz lemma for the holomrophic 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)=α. The sharpness of these inequalities is also proved.

Abstract

In this paper, a boundary version of the Schwarz lemma for the holomrophic 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)=α. The sharpness of these inequalities is also proved.

참고문헌 (20)

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관련 논문AI추천

A SHARP SCHWARZ LEMMA AT THE BOUNDARYBülent Nafi ÖRNEK, Tuğba AKYEL한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제3호On bounds for the derivative of analytic functions at the boundaryBulent Nafi Ornek, Tugba Akyel강원경기수학회 · 한국수학논문집2021 · 제29권 제4호Sharpened forms of the Schwarz lemma on the boundaryBulent Nafi Ornek대한수학회 · 대한수학회보2013 · 제50권 제6호A SHARP SCHWARZ AND CARATHEODORY INEQUALITY ON THE BOUNDARYBülent Nafi ÖRNEK대한수학회 · 대한수학회논문집2014 · 제29권 제1호Results associated with the Schwarz lemma on the boundaryBulent Nafi Ornek대한수학회 · 대한수학회논문집2023 · 제38권 제2호Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit discB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회보2016 · 제53권 제2호

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