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arXiv · 1712.08931

Limits of maximal monotone operators driven by their representative functions

Yboon Garcia·Marc Lassonde
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Abstract

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.

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Yboon Garcia, Marc Lassonde. 2017-12-24. Limits of maximal monotone operators driven by their representative functions. https://arxiv.org/abs/1712.08931

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