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Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings

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  • Tanakit Thianwan

Abstract

We study weak convergence of the projection type Ishikawa iteration scheme for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach space ð ¸ which has a Fréchet differentiable norm or its dual ð ¸ âˆ— has the Kadec-Klee property. Moreover, weak convergence of projection type Ishikawa iterates of two asymptotically nonexpansive nonself-mappings without any condition on the rate of convergence associated with the two maps in a uniformly convex Banach space is established. Weak convergence theorem without making use of any of the Opial's condition, Kadec-Klee property, or Fréchet differentiable norm is proved. Some results have been obtained which generalize and unify many important known results in recent literature.

Suggested Citation

  • Tanakit Thianwan, 2011. "Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-19, October.
    • Handle: RePEc:hin:jnlaaa:745451
    DOI: 10.1155/2011/745451
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