The Equivalence of Convergence Results of Modified Mann and Ishikawa Iterations with Errors without Bounded Range Assumption

Zhiqun Xue, Yaning Wang and Haiyun Zhou

Abstract and Applied Analysis, 2012, vol. 2012, 1-15

Abstract:

Let be an arbitrary uniformly smooth real Banach space, let be a nonempty closed convex subset of , and let be a uniformly generalized Lipschitz generalized asymptotically -strongly pseudocontractive mapping with . Let be four real sequences in and satisfy the conditions: (i) , ; (ii) as and ; (iii) . For some , let be any bounded sequences in , and let be the modified Ishikawa and Mann iterative sequences with errors, respectively. Then the convergence of is equivalent to that of .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:909187

DOI: 10.1155/2012/909187

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