Displaying similar documents to “On a family of quasi-arithmetic means.”

Invariance in the class of weighted quasi-arithmetic means

Justyna Jarczyk, Janusz Matkowski (2006)

Annales Polonici Mathematici

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Under the assumption of twice continuous differentiability of some of the functions involved we determine all the weighted quasi-arithmetic means M,N,K such that K is (M,N)-invariant, that is, K∘(M,N) = K. Some applications to iteration theory and functional equations are presented.

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.