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Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces

✍ Scribed by Bancha Panyanak

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
193 KB
Volume
54
Category
Article
ISSN
0898-1221

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✦ Synopsis

Let K be a nonempty compact convex subset of a uniformly convex Banach space, and T : K β†’ P(K ) a multivalued nonexpansive mapping. We prove that the sequences of Mann and Ishikawa iterates converge to a fixed point of T . This generalizes former results proved by Sastry and Babu [K.P.R. Sastry, G.V.R. Babu, Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point, Czechoslovak Math. J. 55 (2005) 817-826]. We also introduce both of the iterative processes in a new sense, and prove a convergence theorem of Mann iterates for a mapping defined on a noncompact domain.

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✍ Dingping Wu; Shi-Sen Chang; George Yuan πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 117 KB

The purpose of this paper is to study the convergence of the Ishikawa and Mann iterative sequences with mixed errors to approximate the solutions of nonlinear operator equations with perturbed maccretive mappings in arbitrary Banach spaces. The results presented in this paper extend and improve some