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Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi- -Asymptotically Nonexpansive Mappings

Author

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  • Siwaporn Saewan
  • Poom Kumam

Abstract

We introduce a modified block hybrid projection algorithm for solving the convex feasibility problems for an infinite family of closed and uniformly quasi- -asymptotically nonexpansive mappings and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results.

Suggested Citation

  • Siwaporn Saewan & Poom Kumam, 2010. "Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi- -Asymptotically Nonexpansive Mappings," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-22, July.
    • Handle: RePEc:hin:jnlaaa:357120
    DOI: 10.1155/2010/357120
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    Cited by:

    1. Kriengsak Wattanawitoon & Poom Kumam, 2012. "A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Yekini Shehu, 2010. "A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. Fang Zhang & Huan Zhang & Yulong Zhang, 2013. "New Iterative Algorithm for Two Infinite Families of Multivalued Quasi‐Nonexpansive Mappings in Uniformly Convex Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    4. Hecai Yuan & Guohong Shi, 2012. "Approximation of Solutions of an Equilibrium Problem in a Banach Space," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Zi-Ming Wang & Poom Kumam, 2013. "Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Zhaoli Ma & Lin Wang & Yunhe Zhao, 2012. "Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi‐ϕ‐Asymptotically Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Siwaporn Saewan & Poom Kumam, 2010. "A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi‐Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).

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