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Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings

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  • Yuanheng Wang

Abstract

In the framework of a real Banach space with uniformly Gateaux differentiable norm, some new viscosity iterative sequences {xn} are introduced for an infinite family of asymptotically nonexpansive mappings Tii=1∞ in this paper. Under some appropriate conditions, we prove that the iterative sequences {xn} converge strongly to a common fixed point of the mappings Tii=1∞, which is also a solution of a variational inequality. Our results extend and improve some recent results of other authors.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:809528
    DOI: 10.1155/2014/809528
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    References listed on IDEAS

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    1. 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).
    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, Hindawi, vol. 2013, pages 1-7, July.
    3. 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, Hindawi, vol. 2013, pages 1-7, March.
    4. 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).
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