Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces
Let K be a nonempty compact convex subset of a uniformly convex Banach space, and T : K → 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....
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| Format: | Journal |
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2018
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| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=34547143239&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60980 |
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| Institution: | Chiang Mai University |
| Summary: | Let K be a nonempty compact convex subset of a uniformly convex Banach space, and T : K → 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. © 2007 Elsevier Ltd. All rights reserved. |
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