Iterative Algorithms for General Multivalued Variational Inequalities
We introduce and study some new classes of variational inequalities and the Wiener-Hopf equations. Using essentially the projection technique, we establish the equivalence between these problems. This equivalence is used to suggest and analyze some iterative methods for solving the general multivalu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/768272 |
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| _version_ | 1832550276458872832 |
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| author | Yonghong Yao Muhammad Aslam Noor Yeong-Cheng Liou Shin Min Kang |
| author_facet | Yonghong Yao Muhammad Aslam Noor Yeong-Cheng Liou Shin Min Kang |
| author_sort | Yonghong Yao |
| collection | DOAJ |
| description | We introduce and study some new classes of variational inequalities and the Wiener-Hopf equations. Using essentially the projection technique, we establish the equivalence between these problems. This equivalence is used to suggest and
analyze some iterative methods for solving the general multivalued variational in
equalities in conjunction with nonexpansive mappings. We prove a strong convergence
result for finding the common element of the set of fixed points of a nonexpansive
mapping and the set of solutions of the general multivalued variational inequalities
under some mild conditions. Several special cases are also discussed. |
| format | Article |
| id | doaj-art-636bcffe9d874e528f7c229217c58300 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-636bcffe9d874e528f7c229217c583002025-02-03T06:07:08ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/768272768272Iterative Algorithms for General Multivalued Variational InequalitiesYonghong Yao0Muhammad Aslam Noor1Yeong-Cheng Liou2Shin Min Kang3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaMathematics Department, College of Science, King Saud University, Riyadh 1145, Saudi ArabiaDepartment of Information Management, Cheng Shiu University, Kaohsiung 833, TaiwanDepartment of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of KoreaWe introduce and study some new classes of variational inequalities and the Wiener-Hopf equations. Using essentially the projection technique, we establish the equivalence between these problems. This equivalence is used to suggest and analyze some iterative methods for solving the general multivalued variational in equalities in conjunction with nonexpansive mappings. We prove a strong convergence result for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general multivalued variational inequalities under some mild conditions. Several special cases are also discussed.http://dx.doi.org/10.1155/2012/768272 |
| spellingShingle | Yonghong Yao Muhammad Aslam Noor Yeong-Cheng Liou Shin Min Kang Iterative Algorithms for General Multivalued Variational Inequalities Abstract and Applied Analysis |
| title | Iterative Algorithms for General Multivalued
Variational Inequalities |
| title_full | Iterative Algorithms for General Multivalued
Variational Inequalities |
| title_fullStr | Iterative Algorithms for General Multivalued
Variational Inequalities |
| title_full_unstemmed | Iterative Algorithms for General Multivalued
Variational Inequalities |
| title_short | Iterative Algorithms for General Multivalued
Variational Inequalities |
| title_sort | iterative algorithms for general multivalued variational inequalities |
| url | http://dx.doi.org/10.1155/2012/768272 |
| work_keys_str_mv | AT yonghongyao iterativealgorithmsforgeneralmultivaluedvariationalinequalities AT muhammadaslamnoor iterativealgorithmsforgeneralmultivaluedvariationalinequalities AT yeongchengliou iterativealgorithmsforgeneralmultivaluedvariationalinequalities AT shinminkang iterativealgorithmsforgeneralmultivaluedvariationalinequalities |