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Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings. (English) Zbl 1162.65030

The following iterative procedure is studied

x n+1 =α n f(x n )+β n x n +(1-α n -β n )W n x n

where x 0 is arbitrary. The authors prove that if f is contractive and some other conditions are fulfilled the sequence x n converges strongly to the solution of a variational inequality.

MSC:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
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