Averaging operators and set-valued maps

Valov, Vesko. "Averaging operators and set-valued maps." Mathematica Balkanica New Series 28.1-2 (2014): 43-57. <http://eudml.org/doc/281484>.

@article{Valov2014,
abstract = {MSC 2010: 54C35, 54C60.We investigate maps admitting, in general, non-linear averaging operators. Characterizations of maps admitting a normed, weakly additive averaging operator which preserves max (resp., min) and weakly preserves min (resp., max) is obtained. We also describe set-valued maps into completely metrizable spaces admitting lower semi-continuous selections. As a corollary, we obtain a description of surjective maps with a metrizable kernel and complete fibers which admit regular linear averaging operators.},
author = {Valov, Vesko},
journal = {Mathematica Balkanica New Series},
keywords = {Averaging operators; lower semi-continuous maps and functions; preserving minimum and maximum functionals; selections},
language = {eng},
number = {1-2},
pages = {43-57},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {Averaging operators and set-valued maps},
url = {http://eudml.org/doc/281484},
volume = {28},
year = {2014},
}

TY - JOUR
AU - Valov, Vesko
TI - Averaging operators and set-valued maps
JO - Mathematica Balkanica New Series
PY - 2014
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 28
IS - 1-2
SP - 43
EP - 57
AB - MSC 2010: 54C35, 54C60.We investigate maps admitting, in general, non-linear averaging operators. Characterizations of maps admitting a normed, weakly additive averaging operator which preserves max (resp., min) and weakly preserves min (resp., max) is obtained. We also describe set-valued maps into completely metrizable spaces admitting lower semi-continuous selections. As a corollary, we obtain a description of surjective maps with a metrizable kernel and complete fibers which admit regular linear averaging operators.
LA - eng
KW - Averaging operators; lower semi-continuous maps and functions; preserving minimum and maximum functionals; selections
UR - http://eudml.org/doc/281484
ER -