The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ -strongly accretive operators in uniformly smooth Banach spaces

Zeqing Liu, Li Wang, Jeong Sheok Ume and Shin Min Kang

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-12

Abstract:

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ -strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for φ -pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve the corresponding results in the literature.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:069542

DOI: 10.1155/IJMMS/2006/69542

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