On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain th...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/207845 |
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| _version_ | 1832558926603747328 |
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| author | Marwan Amin Kutbi Wutiphol Sintunavarat |
| author_facet | Marwan Amin Kutbi Wutiphol Sintunavarat |
| author_sort | Marwan Amin Kutbi |
| collection | DOAJ |
| description | We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem. |
| format | Article |
| id | doaj-art-4b3fd563aad94a748152eae50869af1e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4b3fd563aad94a748152eae50869af1e2025-02-03T01:31:11ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/207845207845On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone MappingMarwan Amin Kutbi0Wutiphol Sintunavarat1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12121, ThailandWe introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.http://dx.doi.org/10.1155/2013/207845 |
| spellingShingle | Marwan Amin Kutbi Wutiphol Sintunavarat On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping Abstract and Applied Analysis |
| title | On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping |
| title_full | On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping |
| title_fullStr | On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping |
| title_full_unstemmed | On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping |
| title_short | On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping |
| title_sort | on the solution existence of variational like inequalities problems for weakly relaxed η α monotone mapping |
| url | http://dx.doi.org/10.1155/2013/207845 |
| work_keys_str_mv | AT marwanaminkutbi onthesolutionexistenceofvariationallikeinequalitiesproblemsforweaklyrelaxedēamonotonemapping AT wutipholsintunavarat onthesolutionexistenceofvariationallikeinequalitiesproblemsforweaklyrelaxedēamonotonemapping |