On an elementary inclusion problem and generalized weighted quasi-arithmetic means

Zoltán Daróczy; Zsolt Páles

Banach Center Publications, Tome 99 (2013), p. 45-54 / Harvested from The Polish Digital Mathematics Library

Résumé

The aim of this note is to characterize the real coefficients p₁,...,pₙ and q₁,...,qₖ so that $\sum_{i = 1}^{n} p_{i} x_{i} + \sum_{j = 1}^{k} q_{j} y_{j} \in c o n v x ₁, . . ., x ₙ$ be valid whenever the vectors x₁,...,xₙ, y₁,...,yₖ satisfy y₁,...,yₖ ⊆ convx₁,...,xₙ. Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.

Publié le : 2013-01-01

Zbl 1281.39020

EUDML-ID : urn:eudml:doc:282409

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     author = {Zolt\'an Dar\'oczy and Zsolt P\'ales},
     title = {On an elementary inclusion problem and generalized weighted quasi-arithmetic means},
     journal = {Banach Center Publications},
     volume = {99},
     year = {2013},
     pages = {45-54},
     zbl = {1281.39020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc99-0-4}
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Zoltán Daróczy; Zsolt Páles. On an elementary inclusion problem and generalized weighted quasi-arithmetic means. Banach Center Publications, Tome 99 (2013) pp. 45-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc99-0-4/