Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 20 (2013), No. 1, 025--042Copyright Heldermann Verlag 2013 Smooth Selections of Convex-Valued Multifunctions Jacek Sadowski Faculty of Mathematics, Politechnika Warszawska, ul. Koszykowa 75, 00-662 Warszawa, Poland j.sadowski@mini.pw.edu.pl [Abstract-pdf] 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 [ Fulltext-pdf  (187  KB)] for subscribers only.