Journal of Convex Analysis 16 (2009), No. 3, 713--725
Copyright Heldermann Verlag 2009
On Two Properties of Enlargements of Maximal Monotone Operators
Radu Ioan Bot
Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany
radu.bot@mathematik.tu-chemnitz.de
Ernö Robert Csetnek
Faculty of Mathematics, University of Technology, 09107 Chemnitz, Germany
robert.csetnek@mathematik.tu-chemnitz.de
[Abstract-pdf]
We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator $S:X\rightrightarrows X^*$ by $S^{se}$, the smallest enlargement belonging to a certain class of enlargements associated to $S$. Moreover, we prove the weak$^*$ closedness of the set $S_{h_S}(\varepsilon_1,x)+T_{h_T} (\varepsilon_2,x)$ under a weak generalized interior regularity condition.
Keywords: Monotone operator, Fitzpatrick function, representative function, enlargement, subdifferential.
MSC: 47H05, 46N10, 42A50
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