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Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings

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  • Chang-He Xiang
  • Jiang-Hua Zhang
  • Zhe Chen

Abstract

Suppose that E is a real normed linear space, C is a nonempty convex subset of E, T : C → C is a Lipschitzian mapping, and x* ∈ C is a fixed point of T. For given x0 ∈ C, suppose that the sequence {xn} ⊂ C is the Mann iterative sequence defined by xn+1 = (1 − αn)xn + αnTxn, n ≥ 0, where {αn} is a sequence in [0, 1], ∑n=0∞αn2

Suggested Citation

  • Chang-He Xiang & Jiang-Hua Zhang & Zhe Chen, 2012. "Necessary and Sufficient Condition for Mann Iteration Converges to a Fixed Point of Lipschitzian Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:327878
    DOI: 10.1155/2012/327878
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