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Title: Averaging operators and set-valued maps
Authors: Valov, Vesko
Keywords: Averaging operators
lower semi-continuous maps and functions
preserving minimum and maximum functionals
Issue Date: 2014
Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics
Citation: Mathematica Balkanica New Series, Vol. 28, Fasc 1-2 (2014), 43p-57p
Abstract: 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.
Description: MSC 2010: 54C35, 54C60.
ISSN: 0205-3217
Appears in Collections:Mathematica Balkanica New Series, Vol. 28, 2014, Fasc. 1-2

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