Graphical convergence of sums of monotone mappings
Teemu Pennanen, Ralph Tyrrell Rockafellar, Michel A. Théra · Proceedings of the American Mathematical Society · 2002
This paper gives sufficient conditions for graphical convergence of sums of maximal monotone mappings. The main result concerns finite-dimensional spaces and it generalizes known convergence results for sums. The proof is based on a duality argument and a new boundedness result for sequences of monotone mappings which is of interest on its own. An application to the epi-convergence theory of convex functions is given. Counterexamples are used to show that the results cannot be directly extended to infinite dimensions.