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Strong convergence theorems for nonexpansive mappings and Ky Fan inequalities. (English) Zbl 1270.90100
The author introduces a new iteration method and proves strong convergence theorems for finding a common element of the set of fixed points of a nonexpansive mapping and the solution set of a monotone and Lipschitz-type continuous Ky Fan inequality. Under certain conditions on the parameters, the author shows that the iteration sequences generated by this method converge strongly to the common element in a real Hilbert space. Some preliminary computational experiences are reported.

MSC:
90C48Programming in abstract spaces
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References:
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