Abstract

We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator S:X⇉X∗S:X\rightrightarrows X^* by SseS^{se}, the smallest enlargement belonging to a certain class of enlargements associated to SS. Moreover, we prove the weak∗^* closedness of the set ShS(ε1,x)+ThT(ε2,x)S_{h_S}(\varepsilon_1,x)+T_{h_T} (\varepsilon_2,x) under a weak generalized interior regularity condition.

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Keywords

  • Monotone operator
  • Fitzpatrick function
  • representative function
  • enlargement
  • subdifferential

Mathematics Subject Classification

47H05, 46N10, 42A50

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Suggested citation

R. I. Boţ, E. R. Csetnek. “On Two Properties of Enlargements of Maximal Monotone Operators.” Journal of Convex Analysis 16 (2009), No. 3&4, 713–725. https://doi.org/10.68381/jca16043

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press LLC.