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Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings

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  • Jong Soo Jung

Abstract

We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.

Suggested Citation

  • Jong Soo Jung, 2009. "Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-17, June.
    • Handle: RePEc:hin:jnlaaa:573156
    DOI: 10.1155/2009/573156
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