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We propose a flexible approach for computing the resolvent of the sum ofweakly monotone operators in real Hilbert spaces. This relies on splittingmethods where strong convergence is guaranteed. We also prove linearconvergence under Lipschitz continuity assumption. The approach is then appliedto computing the proximity operator of the sum of weakly convex functions, andparticularly to finding the best approximation to the intersection of convexsets.

Computing the resolvent of the sum of operators with application to best approximation problems