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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th-cmuir.6653943832-609802018-09-10T04:06:48Z Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces Bancha Panyanak Computer Science Mathematics 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. 2018-09-10T04:02:23Z 2018-09-10T04:02:23Z 2007-09-01 Journal 08981221 2-s2.0-34547143239 10.1016/j.camwa.2007.03.012 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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Computer Science Mathematics Bancha Panyanak Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces |
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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. |
| format |
Journal |
| author |
Bancha Panyanak |
| author_facet |
Bancha Panyanak |
| author_sort |
Bancha Panyanak |
| title |
Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces |
| title_short |
Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces |
| title_full |
Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces |
| title_fullStr |
Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces |
| title_full_unstemmed |
Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces |
| title_sort |
mann and ishikawa iterative processes for multivalued mappings in banach spaces |
| publishDate |
2018 |
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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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