Abstract
In this paper, we introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Hilbert space, which solves a corresponding variational inequality. Furthermore, we propose explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem. Our results improve and generalize some known results in the current literature. MSC:47H10, 37C25.
Highlights
A viscosity approximation method for finding fixed points of nonexpansive mappings was first proposed by Moudafi in [ ]
In, Xu [ ] proved the strong convergence of the sequence generated by the viscosity approximation method to a unique solution of a certain variational inequality problem defined on the set of fixed points of a nonexpansive map
The purpose of this paper is to introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Hilbert space
Summary
A viscosity approximation method for finding fixed points of nonexpansive mappings was first proposed by Moudafi in [ ]. In , Xu [ ] proved the strong convergence of the sequence generated by the viscosity approximation method to a unique solution of a certain variational inequality problem defined on the set of fixed points of a nonexpansive map. In , Xu [ ] introduced an iterative method for computing the approximate solutions of a quadratic minimization problem over the set of fixed points of a nonexpansive mapping defined on a real Hilbert space. He proved that the sequence generated by the proposed method converges strongly to the unique solution of the quadratic minimization problem.
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