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Displaying similar documents to “Invariance in the class of weighted quasi-arithmetic means”

Remarks on the comparison of weighted quasi-arithmetic means

Gyula Maksa, Zsolt Páles (2010)

Colloquium Mathematicae

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We present comparison theorems for the weighted quasi-arithmetic means and for weighted Bajraktarević means without supposing in advance that the weights are the same.

An extension theorem for a Matkowski-Sutô problem

Zoltán Daróczy, Gabriella Hajdu, Che Tat Ng (2003)

Colloquium Mathematicae

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Let I be an interval, 0 < λ < 1 be a fixed constant and A(x,y) = λx + (1-λ)y, x,y ∈ I, be the weighted arithmetic mean on I. A pair of strict means M and N is complementary with respect to A if A(M(x,y),N(x,y)) = A(x,y) for all x, y ∈ I. For such a pair we give results on the functional equation f(M(x,y)) = f(N(x,y)). The equation is motivated by and applied to the Matkowski-Sutô problem on complementary weighted quasi-arithmetic means M and N.

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

Zoltán Daróczy, Zsolt Páles (2013)

Banach Center Publications

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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 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.