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Journal of Convex Analysis 12 (2005), No. 1, 213--219
Copyright Heldermann Verlag 2005

On the Weak* Convergence of Subdifferentials of Convex Functions

Dariusz Zagrodny
Faculty of Mathematics, Cardinal S. Wyszynski University, Dewajtis 5, 01-815 Warsaw, Poland


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 $x^*$.

Keywords: Subdifferentials, convex function, Attouch's theorem.

MSC: 49J52

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