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A bound of the exterior arcs for a univalent mapping

  • Yu. A. Litvinchuk
  • I. M. Milin
Article
  • 26 Downloads

Abstract

In this paper we consider the intersection of the circle ¦w|=x with the image of the disc ¦z|&#x2264;r, 0<r<1, under the mapping of a function of the formf(z)=z+c2z2+... which is univalent analytic in ¦z|<1. Earlier I. E. Bazilevich proved that for x≥cπ/er the measure of the above intersection does not exceed the measure of the intersection produced by the functionf*(z)=z/(1−ηz)2, η¦=1. In this paper I. E. Bazilevich's ideas are used to strengthen some of his results.

Keywords

Univalent Mapping 
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Literature cited

  1. 1.
    G. M. Goluzin, “On distortion and coefficient theorems for univalent functions,” Matem. Sb.,19, No. 2, 183–202 (1946).Google Scholar
  2. 2.
    I. E. Bazilevich, “On distortion and coefficient theorems for univalent functions,” Matem. Sb.,28, No. 1, 147–164 (1951).Google Scholar
  3. 3.
    N. A. Lebedev and I. M. Milin, “On coefficients of some classes of analytic functions,” Matem. Sb.,28, No. 2, 359–400 (1951).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Yu. A. Litvinchuk
    • 1
  • I. M. Milin
    • 1
  1. 1.VNII MikhanobrUSSR

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