Generalized Weighted Arithmetic Means

Janusz Matkowski (j.matkowski@wmie.uz.zgora.pl)
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Janusz Matkowski: University of Zielona Góra

Chapter Chapter 36 in Functional Equations in Mathematical Analysis, 2011, pp 563-582 from Springer

Abstract: 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.

Keywords: Mean; Generalized weighted mean; Mean-convex function mean-affine functions; Subadditivity; Subtransitivity; Functional equation; Functional inequalities (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4614-0055-4_36

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