Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities
<p>Abstract</p> <p>In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Fixed Point Theory and Applications |
| Subjects: | |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2011/1/55 |
| _version_ | 1819004951994564608 |
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| author | Piri Hossein Badali Ali |
| author_facet | Piri Hossein Badali Ali |
| author_sort | Piri Hossein |
| collection | DOAJ |
| description | <p>Abstract</p> <p>In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for <it>β</it>-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions, we prove the strong convergence theorem for approximating a common element of the above two sets.</p> <p> <b>Mathematics Subject Classification 2000: </b>47H09, 47H10, 43A07, 47J25</p> |
| first_indexed | 2024-12-20T23:45:04Z |
| format | Article |
| id | doaj.art-6239a7b0da6946a59eefc85f329d442c |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-20T23:45:04Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-6239a7b0da6946a59eefc85f329d442c2022-12-21T19:22:58ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122011-01-012011155Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalitiesPiri HosseinBadali Ali<p>Abstract</p> <p>In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for <it>β</it>-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions, we prove the strong convergence theorem for approximating a common element of the above two sets.</p> <p> <b>Mathematics Subject Classification 2000: </b>47H09, 47H10, 43A07, 47J25</p>http://www.fixedpointtheoryandapplications.com/content/2011/1/55projectioncommon fixed pointamenable semigroupiterative processstrong convergencevariational inequality |
| spellingShingle | Piri Hossein Badali Ali Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities Fixed Point Theory and Applications projection common fixed point amenable semigroup iterative process strong convergence variational inequality |
| title | Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities |
| title_full | Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities |
| title_fullStr | Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities |
| title_full_unstemmed | Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities |
| title_short | Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities |
| title_sort | strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities |
| topic | projection common fixed point amenable semigroup iterative process strong convergence variational inequality |
| url | http://www.fixedpointtheoryandapplications.com/content/2011/1/55 |
| work_keys_str_mv | AT pirihossein strongconvergencetheoremforamenablesemigroupsofnonexpansivemappingsandvariationalinequalities AT badaliali strongconvergencetheoremforamenablesemigroupsofnonexpansivemappingsandvariationalinequalities |