Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2018; 33(4): 1205-1215

Online first article April 6, 2018      Printed October 31, 2018

https://doi.org/10.4134/CKMS.c170372

Copyright © The Korean Mathematical Society.

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

B\"{u}lent Nafi \"{O}rnek

Amasya University

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.

Keywords: holomorphic function, Carath\'{e}odory's inequality, angular derivative, Julia-Wolff-lemma, Schwarz lemma

MSC numbers: Primary 30C80, 32A10