An inconsistency equation involving means

Roman Ger; Tomasz Kochanek

Colloquium Mathematicae, Tome 116 (2009), p. 87-99 / Harvested from The Polish Digital Mathematics Library

Résumé

We show that any quasi-arithmetic mean $A_{φ}$ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations $f (M (x, y)) = A_{φ} (f (x), f (y))$ and $f (A_{φ} (x, y)) = M (f (x), f (y))$ are the constant ones.

Publié le : 2009-01-01

Zbl 1168.39006

EUDML-ID : urn:eudml:doc:283809

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     title = {An inconsistency equation involving means},
     journal = {Colloquium Mathematicae},
     volume = {116},
     year = {2009},
     pages = {87-99},
     zbl = {1168.39006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-1-8}
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Roman Ger; Tomasz Kochanek. An inconsistency equation involving means. Colloquium Mathematicae, Tome 116 (2009) pp. 87-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-1-8/