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Convergence of a New Modified Ishikawa Type Iteration for Common Fixed Points of Total Asymptotically Strict Pseudocontractive Semigroups

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  • Yuanheng Wang
  • Chunjie Wang

Abstract

The purpose of this paper is to give a new modified Ishikawa type iteration algorithm for common fixed points of total asymptotically strict pseudocontractive semigroups. Under the reduction of some conditions, both strong convergence and weak convergence of the iteration algorithm are proved in Banach spaces with new methods of proofs, respectively. The main results presented in this paper extend and improve the corresponding recent results of many others.

Suggested Citation

  • Yuanheng Wang & Chunjie Wang, 2013. "Convergence of a New Modified Ishikawa Type Iteration for Common Fixed Points of Total Asymptotically Strict Pseudocontractive Semigroups," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:319241
    DOI: 10.1155/2013/319241
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    References listed on IDEAS

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    1. S. S. Chang & L. Wang & Y. K. Tang & L. Yang, 2012. "The Split Common Fixed Point Problem for Total Asymptotically Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, December.
    2. Wei Xu & Yuanheng Wang, 2012. "Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, October.
    3. Jing Na & Lin Wang & Zhaoli Ma, 2012. "The Split Common Fixed Point Problem for Quasi-Total Asymptotically Nonexpansive Uniformly Lipschitzian Mappings," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, May.
    4. S. S. Chang & L. Wang & Y. K. Tang & L. Yang, 2012. "The Split Common Fixed Point Problem for Total Asymptotically Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Wei Xu & Yuanheng Wang, 2012. "Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Yuanheng Wang, 2014. "Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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