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A sharp Carath\'{e}odory's inequality on the boundary

B\"{u}lent Nafi \"{O}rnek
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회논문집 (Communications of the KMS)|제31권 제3호|pp. 533-547

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참고문헌

키워드

Schwarz lemma on the boundaryholomorphic functionCara\-th\'{e}odory's inequality
주제분류수학

초록

In this paper, a generalized boundary version of Carath\'{e}od\-ory's inequality for holomorphic function satisfying $f(z)=f(0)+a_{p}z^{p}+\cdots,$ and $\Re f(z)\leq A$ for $\left\vert z\right\vert <1$ is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime }(c)$ at the point $c$ with $\Re f(c)=A$. The sharpness of these estimates is also proved.

Abstract

In this paper, a generalized boundary version of Carath\'{e}od\-ory's inequality for holomorphic function satisfying $f(z)=f(0)+a_{p}z^{p}+\cdots,$ and $\Re f(z)\leq A$ for $\left\vert z\right\vert <1$ is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime }(c)$ at the point $c$ with $\Re f(c)=A$. The sharpness of these estimates is also proved.

참고문헌 (19)

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  16. BÜlent Nafi Örnek, "CARATHÉODORY'S INEQUALITY ON THE BOUNDARY", 순수 및 응용수학, 22(2), pp.169~178 (2015), 한국수학교육학회
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관련 논문AI추천

Some results of the Carath\'{e}odory's inequality at the boundaryBulent Nafi Ornek대한수학회 · 대한수학회논문집2018 · 제33권 제4호On bounds for the derivative of analytic functions at the boundaryBulent Nafi Ornek, Tugba Akyel강원경기수학회 · 한국수학논문집2021 · 제29권 제4호Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit discB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회보2016 · 제53권 제2호A SHARP SCHWARZ LEMMA AT THE BOUNDARYBülent Nafi ÖRNEK, Tuğba AKYEL한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제3호A SHARP SCHWARZ AND CARATHEODORY INEQUALITY ON THE BOUNDARYBülent Nafi ÖRNEK대한수학회 · 대한수학회논문집2014 · 제29권 제1호Inequalities for the non-tangential derivative at the boundary for holomorphic functionBulent Nafi Ornek대한수학회 · 대한수학회논문집2014 · 제29권 제3호

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