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 \(H\), \(A:K\rightarrow H\) be inverse strongly monotone, and \(S:K\rightarrow K\) 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.


47H10 Fixed-point theorems
55M20 Fixed points and coincidences in algebraic topology
49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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