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Israel Journal of Mathematics

, Volume 83, Issue 3, pp 289–294 | Cite as

A note on the valence of certain means

  • Zhou Ji
  • Xiao Pingan
Article

Abstract

Given two functionsf(z),g(z) in the (usual) classS, we can form the new functions (arithmetric and geometric mean functions) F(itz)=∝(itf)(itz)+β(itg)(itz) and G(itz)=(itz)(f(itz)/(itz))(su∝)(g(itz)/(itz))(suβ), whereα, β ∈ (0, 1) andα+β=1. This paper determines the maximum valence of the functionsF andG.

Keywords

Unit Circle Unit Disk Negative Integer General Means Large Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    D.A. Brannan and W.K. Hayman,Research problems in complex analysis, Bull. London Math. Soc.21 (1989), 1–35.zbMATHCrossRefMathSciNetGoogle Scholar
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    A.W. Coodman,The valence of sums and products, Can. J. Math.20 (1968), 1173–1177.Google Scholar
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    A.W. Goodman,Univalent Functions, Polygonal Publishing Co. Inc., Washington, New Jersey, 1983.Google Scholar

Copyright information

© Hebrew University 1993

Authors and Affiliations

  • Zhou Ji
    • 1
  • Xiao Pingan
    • 2
  1. 1.Department of Basic ScienceSouthwest Petroleum InstituteNanchongPeople’s Republic of China
  2. 2.Department of MathematicsSichuan Normal UniversityChengduPeople’s Republic of China

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