Geodesic
Smooth Selections of Convex-Valued Multifunctions
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 25-42.

Voir la notice de l'article provenant de la source Heldermann Verlag

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 $x\in X$.
Classification : 26E25, 54C60, 54C65
Mots-clés : Lower semicontinuous multifunction, smooth selection, uniform convergence, approximation, convolution, Castaing representation 
@article{JCA_2013_20_1_JCA_2013_20_1_a2,
     author = {J. Sadowski},
     title = {Smooth {Selections} of {Convex-Valued} {Multifunctions}},
     journal = {Journal of convex analysis},
     pages = {25--42},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a2/}
}
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J. Sadowski. Smooth Selections of Convex-Valued Multifunctions. Journal of convex analysis, Tome 20 (2013) no. 1, pp. 25-42. http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a2/