Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces
Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L≥1, then it is shown that to each Mann iteration there is a Krasnosleskij iteratio...
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| Format: | Article |
| Language: | English |
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2007-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/FPTA/2006/35704 |
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doaj-7cdafde84ef4447b9321d1f37156d2e92020-11-25T00:18:45ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122007-01-01200610.1155/FPTA/2006/35704Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spacesK. N. V. V. Vara PrasadG. V. R. BabuLet E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L≥1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of T.http://dx.doi.org/10.1155/FPTA/2006/35704 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
K. N. V. V. Vara Prasad G. V. R. Babu |
| spellingShingle |
K. N. V. V. Vara Prasad G. V. R. Babu Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces Fixed Point Theory and Applications |
| author_facet |
K. N. V. V. Vara Prasad G. V. R. Babu |
| author_sort |
K. N. V. V. Vara Prasad |
| title |
Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces |
| title_short |
Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces |
| title_full |
Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces |
| title_fullStr |
Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces |
| title_full_unstemmed |
Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces |
| title_sort |
comparison of fastness of the convergence among krasnoselskij, mann, and ishikawa iterations in arbitrary real banach spaces |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2007-01-01 |
| description |
Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L≥1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of T. |
| url |
http://dx.doi.org/10.1155/FPTA/2006/35704 |
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