An extension theorem for a Matkowski-Sutô problem

Zoltán Daróczy; Gabriella Hajdu; Che Tat Ng

Displaying similar documents to “An extension theorem for a Matkowski-Sutô problem”

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.

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.

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 $\sum_{i = 1}^{n} p_{i} x_{i} + \sum_{j = 1}^{k} q_{j} y_{j} \in c o n v x ₁, . . ., x ₙ$ 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.

A functional equation related to an equality of means problem

Janusz Matkowski (2011)

Colloquium Mathematicae

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The functional equation (F(x)-F(y))/(x-y) = (G(x)+G(y))(H(x)+H(y)) where F,G,H are unknown functions is considered. Some motivations, coming from the equality problem for means, are presented.