
Journal of Convex Analysis 20 (2013), No. 1, 025042 Copyright Heldermann Verlag 2013 Smooth Selections of ConvexValued Multifunctions Jacek Sadowski Faculty of Mathematics, Politechnika Warszawska, ul. Koszykowa 75, 00662 Warszawa, Poland j.sadowski@mini.pw.edu.pl [Abstractpdf] We establish a class of multifunctions having smooth ($C^\infty$) selections and formulate assumptions on a multifunction $F$ under which for any continuous selection $f$ of $F$ there is a~sequence of smooth selections of $F$ converging uniformly to $f$. Moreover, we obtain a Castaing type representation of multifunctions by a sequence of smooth selections, i.e. we construct a sequence $\{f_k\}$ of smooth selections of $F$ satisfying the condition $F(x)=\overline{\cup_{k\geq 1} \ f_k(x)}$ for all $x\in X$. Keywords: Lower semicontinuous multifunction, smooth selection, uniform convergence, approximation, convolution, Castaing representation. MSC: 26E25, 54C60, 54C65 [ Fulltextpdf (187 KB)] for subscribers only. 