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A note on the valence of certain means

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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.

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Authors and Affiliations

  1. Department of Basic Science, Southwest Petroleum Institute, 637001, Nanchong, Sichuan, People’s Republic of China

    Zhou Ji

  2. Department of Mathematics, Sichuan Normal University, 610066, Chengdu, Sichuan, People’s Republic of China

    Xiao Pingan

Authors
  1. Zhou Ji
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  2. Xiao Pingan
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Ji, Z., Pingan, X. A note on the valence of certain means. Israel J. Math. 83, 289–294 (1993). https://doi.org/10.1007/BF02784056

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  • DOI: https://doi.org/10.1007/BF02784056

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