Some remarks for $\lambda -$spirallike function of complex order at the boundary of the unit disc
Commun. Korean Math. Soc.
Published online May 13, 2021
Tuğba AKYEL
Maltepe University
Abstract : We consider a different version of Schwarz Lemma for $\lambda-$spirallike function of complex order at the boundary of the unit disc $D.$ We estimate the modulus of the angular derivative of the function $\frac{zf'(z)}{f(z)}$ from below for $\lambda-$spirallike function $f(z)$ of complex order at the boundary of the unit disc $D$ by taking into account the zeros of the function $f(z)-z$ which are different from zero. We also estimate the same function with the second derivatives of the function $f$ at the points $z=0$ and $z=z_0\neq 0.$ We show the sharpness of these estimates and present examples.
Keywords : Angular derivative, Holomorphic function, $\lambda -$spirallike function, Schwarz lemma.
MSC numbers : 30C80, 32A10
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