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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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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