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Estimates for a Certain Subclass of Holomorphic Functions

BÜLENT NAFI ÖRNEK|TUĞBA AKYEL
한국수학교육학회|2019.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제26권 제2호|pp. 59-73|DOI https://doi.org/10.7468/jksmeb.2019.26.2.59

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참고문헌

키워드

holomorphic functionJack's lemmaangular derivative.
주제분류수학

초록

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to N(α) is investigated. For the function f(z) = z + c2z2 + c3z3 + ... which is defined in the unit disc where f(z) ∈ N(α), we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with f(b) = 1 b b ∫ 0 f(t)dt. The sharpness of these inequalities is also proved.

Abstract

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to N(α) is investigated. For the function f(z) = z + c2z2 + c3z3 + ... which is defined in the unit disc where f(z) ∈ N(α), we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with f(b) = 1 b b ∫ 0 f(t)dt. The sharpness of these inequalities is also proved.

참고문헌 (23)

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관련 논문AI추천

Results associated with the Schwarz lemma on the boundaryBulent Nafi Ornek대한수학회 · 대한수학회논문집2023 · 제38권 제2호AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARYBülent Nafi ÖRNEK, Tuğba AKYEL한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제1호Applications of the Schwarz Lemma and Jack’s Lemma for the Holomorphic FunctionsBatuhan Catal, Bulent Nafi Ornek경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit discB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회보2016 · 제53권 제2호Inequalities for the non-tangential derivative at the boundary for holomorphic functionBulent Nafi Ornek대한수학회 · 대한수학회논문집2014 · 제29권 제3호On a Class of Analytic Function related to Schwarz LemmaBülent Nafi ÖRNEK한국수학교육학회 · 이론수학과 교직수학2022 · 제29권 제1호

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