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 A Sharp Schwarz and Carath\'{e}odory inequality on the boundary Commun. Korean Math. Soc. 2014 Vol. 29, No. 1, 75-81 https://doi.org/10.4134/CKMS.2014.29.1.75Printed January 31, 2014 B\"{u}lent Nafi \"{O}rnek Gebze Institute of Technology Abstract : 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 Downloads: Full-text PDF

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