Viscosity approximation methods for nonexpansive mappings and monotone mappings

By Junmin Chen, Li-juan Zhang, Tie-Gang Fan. 2007

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Abstract Viscosity approximation methods for nonexpansive mappings are studied. Consider the iteration process { x n } , where x 0 ∈ C is arbitrary and x n + 1 = α n f ( x n ) + ( 1 − α n ) S P C ( x n − λ n A x n ) , f is a contraction on C, S is a nonexpansive self-mapping of a closed convex subset C of a Hilbert space H. It is shown that { x n } converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/fc6369475ba6d7d5866fcb20fa3359e3c915b394