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

  • Ornek, Bulent Nafi (Department of Mathematics Gebze Institute of Technology)
  • Received : 2014.03.01
  • Published : 2014.07.31

Abstract

In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}$ defined in the unit disc, with ${\Re}\(\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}\)$ > ${\beta}$, $0{\leq}{\beta}$ < 1, $0{\leq}{\lambda}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ${\xi}$, 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

References

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