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Weak convergence theorems for nonexpansive mappings and monotone mappings. (English) Zbl 1055.47052
Let K be a closed convex subset of a real Hilbert space H, A:KH be inverse strongly monotone, and S:KK be nonexpansive. Assuming that the set of solutions of the variational inequality for A and the set of fixed points of S have a nonempty intersection, the authors introduce an iteration process that is shown to generate a sequence converging weakly to an element of this intersection. This is the main result of the paper, which is then applied to obtain a sequence converging to a common fixed point of a nonexpansive map and a strictly pseudocontractive map.

MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
55M20Fixed points and coincidences (algebraic topology)
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators