On axiomizing and extending the quasi-arithmetic mean
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Date
2018
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Abstract
Quasi-arithmetic means contain many other mean value concepts
such as the arithmetic, the geometric or the harmonic mean as
special cases. Treating quasi-arithmetic means as sequences of mappings
from I^n into I (for some real interval I) this paper shows that under
mild additional conditions this mapping is uniquely determined by its
values on I^2. This extends a well-known result by Huntington [4] where
this claim is proven only for special cases.
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Keywords
quasi-arithmetic mean, strong decomposability