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Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions

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  • Wei Xu
  • Yuanheng Wang

Abstract

This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces by yn = βnSxn + (1 − βn)xn, xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and ∀n ≥ 0, where Ti : C ↦ H is a nonself ki‐strictly pseudocontraction. Under certain approximate conditions, the sequence {xn} converges strongly to x*∈⋂i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:457024
    DOI: 10.1155/2012/457024
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    References listed on IDEAS

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    1. Yonghong Yao & Yeong-Cheng Liou, 2010. "Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-19, October.
    2. Yuanheng Wang & Liu Yang, 2012. "Modified Relaxed Extragradient Method for a General System of Variational Inequalities and Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, July.
    3. Yuanheng Wang & Liu Yang, 2012. "Modified Relaxed Extragradient Method for a General System of Variational Inequalities and Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Yonghong Yao & Yeong-Cheng Liou, 2010. "Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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    Cited by:

    1. Yuanheng Wang & Weifeng Xuan, 2013. "Convergence Theorems for Common Fixed Points of a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. 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).
    3. Wei Xu & Yuanheng Wang, 2013. "A General Iterative Algorithm with Strongly Positive Operators for Strict Pseudo‐Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Yuanheng Wang, 2012. "Strong Convergence Theorems for Asymptotically Weak G‐Pseudo‐Ψ‐Contractive Non‐Self‐Mappings with the Generalized Projection in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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