Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces
<p/> <p>We prove that every firmly nonexpansive-like mapping from a closed convex subset <inline-formula> <graphic file="1687-1812-2010-806837-i1.gif"/></inline-formula> of a smooth, strictly convex and reflexive Banach pace into itself has a fixed point if an...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/806837 |
| _version_ | 1818893432437866496 |
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| author | Saejung Satit |
| author_facet | Saejung Satit |
| author_sort | Saejung Satit |
| collection | DOAJ |
| description | <p/> <p>We prove that every firmly nonexpansive-like mapping from a closed convex subset <inline-formula> <graphic file="1687-1812-2010-806837-i1.gif"/></inline-formula> of a smooth, strictly convex and reflexive Banach pace into itself has a fixed point if and only if <inline-formula> <graphic file="1687-1812-2010-806837-i2.gif"/></inline-formula> is bounded. We obtain a necessary and sufficient condition for the existence of solutions of an equilibrium problem and of a variational inequality problem defined in a Banach space.</p> |
| first_indexed | 2024-12-19T18:12:30Z |
| format | Article |
| id | doaj.art-7ca2e769f4cf4cc088d4f559dbc47cb3 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-19T18:12:30Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-7ca2e769f4cf4cc088d4f559dbc47cb32022-12-21T20:11:16ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101806837Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach SpacesSaejung Satit<p/> <p>We prove that every firmly nonexpansive-like mapping from a closed convex subset <inline-formula> <graphic file="1687-1812-2010-806837-i1.gif"/></inline-formula> of a smooth, strictly convex and reflexive Banach pace into itself has a fixed point if and only if <inline-formula> <graphic file="1687-1812-2010-806837-i2.gif"/></inline-formula> is bounded. We obtain a necessary and sufficient condition for the existence of solutions of an equilibrium problem and of a variational inequality problem defined in a Banach space.</p>http://www.fixedpointtheoryandapplications.com/content/2010/806837 |
| spellingShingle | Saejung Satit Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces Fixed Point Theory and Applications |
| title | Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces |
| title_full | Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces |
| title_fullStr | Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces |
| title_full_unstemmed | Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces |
| title_short | Ray's Theorem for Firmly Nonexpansive-Like Mappings and Equilibrium Problems in Banach Spaces |
| title_sort | ray s theorem for firmly nonexpansive like mappings and equilibrium problems in banach spaces |
| url | http://www.fixedpointtheoryandapplications.com/content/2010/806837 |
| work_keys_str_mv | AT saejungsatit raystheoremforfirmlynonexpansivelikemappingsandequilibriumproblemsinbanachspaces |