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Some results of the Carath\'{e}odory's inequality at the boundary

Bulent Nafi Ornek
대한수학회 (The Korean Mathematical Society)|2018.10|대한수학회논문집 (Communications of the KMS)|제33권 제4호|pp. 1205-1215

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참고문헌

키워드

holomorphic functionSchwarz lemmaangular derivativeCarath\'{e}odory's inequalityJulia-Wolff-lemma
주제분류수학

초록

In this paper, a boundary version of the Carath\'{e}odory's inequality is investigated. We shall give an estimate below $\left\vert f^{\prime }(b)\right\vert $ according to the first nonzero Taylor coefficient of about two zeros, namely $z=0$ and $z_{1}\neq 0$. The sharpness of these estimates is also proved.

Abstract

In this paper, a boundary version of the Carath\'{e}odory's inequality is investigated. We shall give an estimate below $\left\vert f^{\prime }(b)\right\vert $ according to the first nonzero Taylor coefficient of about two zeros, namely $z=0$ and $z_{1}\neq 0$. The sharpness of these estimates is also proved.

참고문헌 (22)

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