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Commun. Korean Math. Soc. 2014; 29(1): 75-81
Printed January 31, 2014
https://doi.org/10.4134/CKMS.2014.29.1.75
Copyright © The Korean Mathematical Society.
A Sharp Schwarz and Carath\'{e}odory inequality on the boundary
B\"{u}lent Nafi \"{O}rnek
Gebze Institute of Technology
In this paper, a boundary version of the Schwarz and Carath\-\'{e}odory inequality are investigated. New inequalities of the Carath\'{e}odory's inequality and Schwarz lemma at boundary are obtained by taking into account zeros of $f(z)$ function which are different from zero. The sharpness of these inequalities is also proved.
Keywords: Schwarz lemma on the boundary, holomorphic function, Julia-Wolff-Lemma
MSC numbers: Primary 30C80
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