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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 is a real normed linear space, is a nonempty convex subset of , is a Lipschitzian mapping, and is a fixed point of . For given , suppose that the sequence is the Mann iterative sequence defined by , where is a sequence in [0, 1], , . We prove that the sequence strongly converges to if and only if there exists a strictly increasing function with such that .

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, Hindawi, vol. 2012, pages 1-9, September.
    • Handle: RePEc:hin:jnljam:327878
    DOI: 10.1155/2012/327878
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