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

Zoltán 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 -