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Applications of the Schwarz Lemma and Jack’s Lemma for the Holomorphic Functions

Batuhan Catal|Bulent Nafi Ornek
경북대학교 자연과학대학 수학과|2020.09|Kyungpook Mathematical Journal|제60권 제3호|pp. 507-518|DOI 10.5666/KMJ.2020.60.3.507

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참고문헌

키워드

holomorphic functionangular derivativeJack’s lemmathe Schwarz lemma on the boundary
주제분류수학

초록

We consider a boundary version of the Schwarz Lemma on a certain class of functions which is denoted by N. For the function f(z) = z + a2z2 + a3z3 + ... which is defined in the unit disc D such that the function f(z) belongs to the class N, we estimate from below the modulus of the angular derivative of the function f''(z)/f(z) at the boundary point c with f'(c) = 0. The sharpness of these inequalities is also proved.

Abstract

We consider a boundary version of the Schwarz Lemma on a certain class of functions which is denoted by N. For the function f(z) = z + a2z2 + a3z3 + ... which is defined in the unit disc D such that the function f(z) belongs to the class N, we estimate from below the modulus of the angular derivative of the function f''(z)/f(z) at the boundary point c with f'(c) = 0. The sharpness of these inequalities is also proved.

참고문헌 (20)

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관련 논문AI추천

Applications of Jack's lemma for certain subclasses of holomorphic functions on the unit discBatuhan Catal, Bulent Nafi Ornek대한수학회 · 대한수학회논문집2019 · 제34권 제2호Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit discB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회보2016 · 제53권 제2호Estimates for a Certain Subclass of Holomorphic FunctionsBÜLENT NAFI ÖRNEK, TUĞBA AKYEL한국수학교육학회 · 이론수학과 교직수학2019 · 제26권 제2호AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARYBülent Nafi ÖRNEK, Tuğba AKYEL한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제1호A SHARP SCHWARZ LEMMA AT THE BOUNDARYBülent Nafi ÖRNEK, Tuğba AKYEL한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제3호Applications of the Schwarz Lemma related to Boundary PointsBülent Nafi ÖRNEK한국수학교육학회 · 이론수학과 교직수학2023 · 제30권 제3호

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