On the Weak* Convergence of Subdifferentials of Convex Functions

Abstract

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^*

.

Contact details are reproduced from the original publication and may be historical.

Faculty of Mathematics, Cardinal S. Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland

49J52

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.