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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 $$H$$, $$A:K\rightarrow H$$ 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.

##### MSC:
 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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##### References:
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