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

Zoltán Daróczy, Zsolt Páles (2013)

Banach Center Publications

The aim of this note is to characterize the real coefficients p₁,...,pₙ and q₁,...,qₖ so that i = 1 n p i x i + j = 1 k q j y j c o n v x , . . . , x 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.

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