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

Chang-He Xiang, Jiang-Hua Zhang and Zhe Chen

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

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

Date: 2012
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https://doi.org/10.1155/2012/327878

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:327878

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