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The pointwise sum of maximal monotone operators. (Somme ponctuelle d’opérateurs maximaux monotones.) (French) Zbl 0869.47028

Summary: The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graph convergence of maximal monotone operators to the more general setting of reflexive Banach spaces. In addition, we present some conditions which imply the uniform Brézis-Crandall-Pazy condition. Afterwards, we present, as a consequence, some recent conditions which ensure the Mosco-epiconvergence of the sum of convex proper lower semicontinuous functions.

MSC:

47H05 Monotone operators and generalizations
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54C60 Set-valued maps in general topology
26B25 Convexity of real functions of several variables, generalizations
46B10 Duality and reflexivity in normed linear and Banach spaces
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