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, 1-9

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 .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:327878

DOI: 10.1155/2012/327878

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