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Generalized Weighted Arithmetic Means

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Janusz Matkowski

    (University of Zielona Góra
    Silesian University)

Abstract

Means which are the sum of single variable functions are considered. It is shown among other that if such a mean is weighted quasi-arithmetic, or subtranslative or subadditive then it must be a weighted quasi-arithmetic mean. Conditions under which the functions of the form f(x) = ax + b are affine or convex with respect to such a mean are presented. Invariance of a weighted arithmetic mean with respect to the relevant mean-type mappings is considered. Some open problems are presented.

Suggested Citation

  • Janusz Matkowski, 2011. "Generalized Weighted Arithmetic Means," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 563-582, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_36
    DOI: 10.1007/978-1-4614-0055-4_36
    as

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