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


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.


Unit Circle Unit Disk Negative Integer General Means Large Disk 
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  1. [1]
    D.A. Brannan and W.K. Hayman,Research problems in complex analysis, Bull. London Math. Soc.21 (1989), 1–35.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    D.M. Campbell and V. Singh,Valence properties of the solution of a differential equation, Pacific J. Math.84 (1979), 29–33.MATHMathSciNetGoogle Scholar
  3. [3]
    A.W. Coodman,The valence of sums and products, Can. J. Math.20 (1968), 1173–1177.Google Scholar
  4. [4]
    A.W. Goodman,The valence of certain means, J. Analyse Math.22 (1969), 355–361.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    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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