INEQUALITIES FOR THE NON-TANGENTIAL DERIVATIVE AT THE BOUNDARY FOR HOLOMORPHIC FUNCTION

Title & Authors
INEQUALITIES FOR THE NON-TANGENTIAL DERIVATIVE AT THE BOUNDARY FOR HOLOMORPHIC FUNCTION
Ornek, Bulent Nafi;

Abstract
In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $\small{f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}}$ defined in the unit disc, with $\small{{\Re}$$\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}$$}$ > $\small{{\beta}}$, $\small{0{\leq}{\beta}}$ < 1, $\small{0{\leq}{\lambda}}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point $\small{{\xi}}$, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.
Keywords
Schwarz lemma on the boundary;holomorphic function;second non-tangential derivative;critical points;
Language
English
Cited by
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