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http://dx.doi.org/10.4134/CKMS.c150194

A SHARP CARATHÉODORY'S INEQUALITY ON THE BOUNDARY  

Ornek, Bulent Nafi (Department of Computer Engineering Amasya University)
Publication Information
Communications of the Korean Mathematical Society / v.31, no.3, 2016 , pp. 533-547 More about this Journal
Abstract
In this paper, a generalized boundary version of $Carath{\acute{e}}odory^{\prime}s$ inequality for holomorphic function satisfying $f(z)= f(0)+a_pz^p+{\cdots}$, and ${\Re}f(z){\leq}A$ for ${\mid}z{\mid}$<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.
Keywords
holomorphic function; Schwarz lemma on the boundary; $Carath{\acute{e}}odory^{\prime}s$ inequality;
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Times Cited By KSCI : 5  (Citation Analysis)
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