Averaging operators lower semi-continuous maps and functions preserving minimum and maximum functionals selections
Bulgarian Academy of Sciences - National Committee for Mathematics
Mathematica Balkanica New Series, Vol. 28, Fasc 1-2 (2014), 43p-57p
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.