In a previous paper, the authors showed that in a reflexive Banach space the lower limit of a sequence of maximal monotone operators is always representable by a convex function. The present paper gives precisions to the latter result by demonstrating the continuity of the representation with respect to the epi-convergence of the representative functions, and the stability of the class of maximal monotone operators with respect to the Mosco-convergence of their representative functions.
|Number of pages||9|
|State||Published - 1 Jun 2019|
Bibliographical notePublisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
- Convex function
- Maximal monotone operator
- Representative function