On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces
In the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/671983 |
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| _version_ | 1832550580971634688 |
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| author | Nawab Hussain Giuseppe Marino Badriah A. S. Alamri |
| author_facet | Nawab Hussain Giuseppe Marino Badriah A. S. Alamri |
| author_sort | Nawab Hussain |
| collection | DOAJ |
| description | In the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm. |
| format | Article |
| id | doaj-art-a54dcc4c7da44cedaec56f3f873a23ba |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a54dcc4c7da44cedaec56f3f873a23ba2025-02-03T06:06:24ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/671983671983On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert SpacesNawab Hussain0Giuseppe Marino1Badriah A. S. Alamri2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaIn the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm.http://dx.doi.org/10.1155/2015/671983 |
| spellingShingle | Nawab Hussain Giuseppe Marino Badriah A. S. Alamri On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces Journal of Function Spaces |
| title | On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces |
| title_full | On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces |
| title_fullStr | On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces |
| title_full_unstemmed | On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces |
| title_short | On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces |
| title_sort | on mann s type method for nonexpansive and strongly quasinonexpansive mappings in hilbert spaces |
| url | http://dx.doi.org/10.1155/2015/671983 |
| work_keys_str_mv | AT nawabhussain onmannstypemethodfornonexpansiveandstronglyquasinonexpansivemappingsinhilbertspaces AT giuseppemarino onmannstypemethodfornonexpansiveandstronglyquasinonexpansivemappingsinhilbertspaces AT badriahasalamri onmannstypemethodfornonexpansiveandstronglyquasinonexpansivemappingsinhilbertspaces |