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Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications

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  • Somyot Plubtieng
  • Wanna Sriprad

Abstract

We present two iterative schemes with errors which are proved to be strongly convergent to a common element of the set of fixed points of a countable family of relatively nonexpansive mappings and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space. Using the result we consider strong convergence theorems for variational inequalities and equilibrium problems in a real Hilbert space and strong convergence theorems for maximal monotone operators in a real uniformly smooth and uniformly convex Banach space.

Suggested Citation

  • Somyot Plubtieng & Wanna Sriprad, 2010. "Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-18, December.
    • Handle: RePEc:hin:jnlaaa:301305
    DOI: 10.1155/2010/301305
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