Attouch, H.; Riahi, H.; Théra, M. The pointwise sum of maximal monotone operators. (Somme ponctuelle d’opérateurs maximaux monotones.) (French) Zbl 0869.47028 Serdica Math. J. 22, No. 3, 267-292 (1996). 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. Cited in 10 Documents 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 Keywords:maximality of the pointwise sum; maximal monotone operators; graph convergence; reflexive Banach spaces; uniform Brézis-Crandall-Pazy condition; Mosco-epiconvergence; sum of convex proper lower semicontinuous functions PDFBibTeX XMLCite \textit{H. Attouch} et al., Serdica Math. J. 22, No. 3, 267--292 (1996; Zbl 0869.47028) Full Text: EuDML