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

Banach Center Publications (2013)

- Volume: 99, Issue: 1, page 45-54
- ISSN: 0137-6934

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topZoltán Daróczy, and Zsolt Páles. "On an elementary inclusion problem and generalized weighted quasi-arithmetic means." Banach Center Publications 99.1 (2013): 45-54. <http://eudml.org/doc/282409>.

@article{ZoltánDaróczy2013,

abstract = {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 ⊆ convx₁,...,xₙ.
Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.},

author = {Zoltán Daróczy, Zsolt Páles},

journal = {Banach Center Publications},

keywords = {mean; functional equation; quasi-arithmetic mean; generalized weighted quasi-arithmetic mean},

language = {eng},

number = {1},

pages = {45-54},

title = {On an elementary inclusion problem and generalized weighted quasi-arithmetic means},

url = {http://eudml.org/doc/282409},

volume = {99},

year = {2013},

}

TY - JOUR

AU - Zoltán Daróczy

AU - Zsolt Páles

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

JO - Banach Center Publications

PY - 2013

VL - 99

IS - 1

SP - 45

EP - 54

AB - 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 ⊆ convx₁,...,xₙ.
Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.

LA - eng

KW - mean; functional equation; quasi-arithmetic mean; generalized weighted quasi-arithmetic mean

UR - http://eudml.org/doc/282409

ER -

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