Geodesic
On the Weak* Convergence of Subdifferentials of Convex Functions
Journal of convex analysis, Tome 12 (2005) no. 1, pp. 213-219.

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

Let us assume that a sequence $\{ f_{n} \}_{n=1}^{\infty }$ of proper lower semicontinuous convex functions is bounded on some open subset of a weakly compactly generated Banach space. It is shown that if $\{ f_{n} \}_{n=1}^{\infty }$ is a Mosco converging sequence, then for every subgradient $x^*$ of $f$ at $x$ there are subgradients $x^{*}_{n}\in \partial f_{n}(x_{n})$ such that $\{ x^{*}_{n} \}_{n=1}^{\infty }$ is weakly$^*$ converging to $x^*$.
Classification : 49J52
Mots-clés : Subdifferentials, convex function, Attouch's theorem 
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     author = {D. Zagrodny},
     title = {On the {Weak*} {Convergence} of {Subdifferentials} of {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {213--219},
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     number = {1},
     year = {2005},
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}
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D. Zagrodny. On the Weak* Convergence of Subdifferentials of Convex Functions. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 213-219. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a14/