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Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces

Author

Listed:
  • L. C. Ceng

    (Shanghai Normal University)

  • A. Petruşel

    (Babeş-Bolyai University Cluj-Napoca)

Abstract

This paper deals with a method for approximating a solution of the following problem: find hierarchically a common fixed point of a finite family of nonself nonexpansive mappings with respect to a nonexpansive self mapping on a closed convex subset of a smooth and reflexive Banach space X, which admits a weakly sequentially continuous duality mapping. First, we prove a weak convergence theorem which extends and improves one recent result proved by Yao and Liou (see Inverse Problems 24 (2008), doi: 10.1088/0266-5611/24/1/015015 ). Secondly, when the self mapping is a contraction, we prove, under different restrictions on parameters, a strong convergence result which generalize some recent results in the literature.

Suggested Citation

  • L. C. Ceng & A. Petruşel, 2010. "Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 617-639, September.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:3:d:10.1007_s10957-010-9679-0
    DOI: 10.1007/s10957-010-9679-0
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    References listed on IDEAS

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    1. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    2. L. C. Zeng & J. C. Yao, 2007. "Existence Theorems for Variational Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 321-337, February.
    3. N. N. Tam & J. C. Yao & N. D. Yen, 2008. "Solution Methods for Pseudomonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 253-273, August.
    4. B. T. Kien & M. M. Wong & N. C. Wong & J. C. Yao, 2009. "Solution Existence of Variational Inequalities with Pseudomonotone Operators in the Sense of Brézis," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 249-263, February.
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