Wyniki wyszukiwania

1

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

100%

Daróczy Z., Páles Z.

Banach Center Publications

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2013

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tom 99

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nr 1

45-54

EN

The aim of this note is to characterize the real coefficients p₁,...,pₙ and q₁,...,qₖ so that $∑_{i=1}^{n} p_ix_i + ∑_{j=1}^{k} q_jy_j ∈ conv{x₁,...,xₙ}$ be valid whenever the vectors x₁,...,xₙ, y₁,...,yₖ satisfy {y₁,...,yₖ} ⊆ conv{x₁,...,xₙ}. Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.

2

On a problem of Matkowski

100%

Daróczy Z., Maksa G.

Colloquium Mathematicum

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1999

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tom 82

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nr 1

117-123

EN

We solve Matkowski's problem for strictly comparable quasi-arithmetic means.

3

An extension theorem for a Matkowski-Sutô problem

81%

Daróczy Z., Hajdu G., Ng C.

Colloquium Mathematicum

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2003

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tom 95

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nr 2

153-161

EN

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.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Banach Center Publications

3 Daróczy Z.

1 Hajdu G.

1 Maksa G.

1 Ng C.

1 Páles Z.

1 2013

1 2003

1 1999

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

On a problem of Matkowski

An extension theorem for a Matkowski-Sutô problem