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Strong Convergence Theorems for a Countable Family of Total Quasi‐ϕ‐Asymptotically Nonexpansive Nonself Mappings

Author

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  • Liang-cai Zhao
  • Shih-sen Chang

Abstract

The purpose of this paper is to introduce a class of total quasi‐ϕ‐asymptotically nonexpansive‐nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.

Suggested Citation

  • Liang-cai Zhao & Shih-sen Chang, 2012. "Strong Convergence Theorems for a Countable Family of Total Quasi‐ϕ‐Asymptotically Nonexpansive Nonself Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:136134
    DOI: 10.1155/2012/136134
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    References listed on IDEAS

    as
    1. Kriengsak Wattanawitoon & Poom Kumam, 2012. "The Modified Block Iterative Algorithms for Asymptotically Relatively Nonexpansive Mappings and the System of Generalized Mixed Equilibrium Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Preedaporn Kanjanasamranwong & Poom Kumam & Siwaporn Saewan, 2012. "A Modified Halpern‐TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi‐ϕ‐Asymptotically Nonexpansive Mapping in a Banach Space," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Xiaolong Qin & Jong Kyu Kim & Tianze Wang, 2011. "On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    4. Kriengsak Wattanawitoon & Poom Kumam, 2012. "The Modified Block Iterative Algorithms for Asymptotically Relatively Nonexpansive Mappings and the System of Generalized Mixed Equilibrium Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, July.
    5. Preedaporn Kanjanasamranwong & Poom Kumam & Siwaporn Saewan, 2012. "A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi- ð “ -Asymptotically Nonexpansive Mapping in a Banach Space," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, June.
    6. Xiaolong Qin & Jong Kyu Kim & Tianze Wang, 2011. "On the Convergence of Implicit Iterative Processes for Asymptotically Pseudocontractive Mappings in the Intermediate Sense," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-18, April.
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