Geodesic
Smooth Selections of Convex-Valued Multifunctions
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 25-42 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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},
     year = {2013},
     volume = {20},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a2/}
}
TY  - JOUR
AU  - J. Sadowski
TI  - Smooth Selections of Convex-Valued Multifunctions
JO  - Journal of convex analysis
PY  - 2013
SP  - 25
EP  - 42
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a2/
ID  - JCA_2013_20_1_JCA_2013_20_1_a2
ER  - 
%0 Journal Article
%A J. Sadowski
%T Smooth Selections of Convex-Valued Multifunctions
%J Journal of convex analysis
%D 2013
%P 25-42
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a2/
%F JCA_2013_20_1_JCA_2013_20_1_a2
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/