Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOME REMARKS FOR λ-SPIRALLIKE FUNCTION OF COMPLEX ORDER AT THE BOUNDARY OF THE UNIT DISC

  • Akyel, Tugba (The Faculty of Engineering and Natural Sciences Maltepe University)
  • Received : 2020.09.08
  • Accepted : 2021.01.20
  • Published : 2021.10.31
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Abstract

We consider a different version of Schwarz Lemma for λ-spirallike function of complex order at the boundary of the unit disc D. We estimate the modulus of the angular derivative of the function $\frac{zf^{\prime}(z)}{f(z)}$ from below for λ-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 = z0 ≠ 0. We show the sharpness of these estimates and present examples.

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References

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