Mixed quasi invex equilibrium problems
We introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204310112 |
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| _version_ | 1832563821987758080 |
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| author | Muhammad Aslam Noor |
| author_facet | Muhammad Aslam Noor |
| author_sort | Muhammad Aslam Noor |
| collection | DOAJ |
| description | We introduce a new class of equilibrium problems, known as
mixed quasi invex equilibrium (or
equilibrium-like) problems. This class of invex
equilibrium problems includes equilibrium
problems, variational inequalities, and
variational-like inequalities as special cases. Several iterative
schemes for solving invex equilibrium problems are suggested and
analyzed using the auxiliary principle technique. It is shown
that the convergence of these iterative schemes requires either
pseudomonotonicity or partially relaxed strong monotonicity,
which are weaker conditions than the previous ones. As special
cases, we also obtained the correct forms of the algorithms for
solving variational-like inequalities, which have been considered
in the setting of convexity. In fact, our results represent
significant and important refinements of the previously known
results. |
| format | Article |
| id | doaj-art-0a2c2ded64ef44b28fecba7a1e077526 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0a2c2ded64ef44b28fecba7a1e0775262025-02-03T01:12:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004573057306710.1155/S0161171204310112Mixed quasi invex equilibrium problemsMuhammad Aslam Noor0Etisalat College of Engineering, P.O. Box 980, Sharjah, United Arab EmiratesWe introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational-like inequalities as special cases. Several iterative schemes for solving invex equilibrium problems are suggested and analyzed using the auxiliary principle technique. It is shown that the convergence of these iterative schemes requires either pseudomonotonicity or partially relaxed strong monotonicity, which are weaker conditions than the previous ones. As special cases, we also obtained the correct forms of the algorithms for solving variational-like inequalities, which have been considered in the setting of convexity. In fact, our results represent significant and important refinements of the previously known results.http://dx.doi.org/10.1155/S0161171204310112 |
| spellingShingle | Muhammad Aslam Noor Mixed quasi invex equilibrium problems International Journal of Mathematics and Mathematical Sciences |
| title | Mixed quasi invex equilibrium problems |
| title_full | Mixed quasi invex equilibrium problems |
| title_fullStr | Mixed quasi invex equilibrium problems |
| title_full_unstemmed | Mixed quasi invex equilibrium problems |
| title_short | Mixed quasi invex equilibrium problems |
| title_sort | mixed quasi invex equilibrium problems |
| url | http://dx.doi.org/10.1155/S0161171204310112 |
| work_keys_str_mv | AT muhammadaslamnoor mixedquasiinvexequilibriumproblems |