대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제36권4호
  • /
  • Pages.763-770
  • /
  • 1999
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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MEROMOR0PHIC UNIVALENT HARMONIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

  • 발행 : 1999.11.01
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초록

The purpose of this paper is to give sufficient coefficient conditions for a class of univalent harmonic functions that map each $$\mid$z$\mid$$ = r >1 onto a curve that bounds a domain that is starlike with respect to origin. Furthermore, it is shown that these conditions are also necessary when the coefficients are negative. Extreme points for these classes are also determined. Finally, comparable results are given for the convex analgo.

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참고문헌

  1. Ann. Acad. Sci. Fenn. Ser Al Math. v.9 Harmonic Univalent Functions J. Clunie;T. Sheill-Small
  2. Univalent Functions P. L. Duren
  3. Trans. Amer. Math. Soc. v.299 W. Hengartner;G. Schober
  4. J. Korean Math. Soc. v.32 no.4 Planar harmonic mappings and curvature estimates S. H. Jun
  5. J. London Math. Soc. v.42 no.2 Constants for planar harmonic mappings T. Sheil-Small
  6. J. Math. Anal. Appl. v.220 Harmonic univalent functions negative coefficients H. Silverman