Systems of quasi-equilibrium problems with lower and upper bounds
In this work, we consider systems of quasi-equilibrium problems with lower and upper bounds and establish the existence of their solutions by using some known maximal element theorems for a family of multivalued maps. Our problems are more general than the one posed in [G. Isac, V.M. Sehgal, S.P. Si...
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| Published in | Applied mathematics letters Vol. 20; no. 3; pp. 323 - 328 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.03.2007
Elsevier |
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| Abstract | In this work, we consider systems of quasi-equilibrium problems with lower and upper bounds and establish the existence of their solutions by using some known maximal element theorems for a family of multivalued maps. Our problems are more general than the one posed in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. As a particular case, we also get the answer to the problem raised in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. |
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| AbstractList | In this work, we consider systems of quasi-equilibrium problems with lower and upper bounds and establish the existence of their solutions by using some known maximal element theorems for a family of multivalued maps. Our problems are more general than the one posed in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. As a particular case, we also get the answer to the problem raised in [G. Isac, V.M. Sehgal, S.P. Singh, An alternative version of a variational inequality, Indian J. Math. 41 (1999) 25–31]. |
| Author | Al-Homidan, Suliman Ansari, Qamrul Hasan |
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| Cites_doi | 10.12775/TMNA.2000.016 10.1016/S0022-247X(03)00385-8 10.1023/A:1024971128483 10.1016/j.jmaa.2004.03.067 10.1080/00036810008840877 10.1006/jmaa.1998.5964 10.2140/pjm.1974.54.17 10.1016/S0893-9659(99)00062-2 10.1006/jmaa.1999.6311 10.1016/S0893-9659(00)00032-X 10.1007/BF02192244 10.1023/A:1022666014055 10.1006/jmaa.1996.0007 10.1016/S0893-9659(01)00139-2 10.1023/A:1006095413166 10.1090/S0002-9939-98-04347-0 |
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| Keywords | Maximal element theorems System of quasi-equilibrium problems System of generalized implicit quasi-equilibrium problems Lower and upper bounds Lower bound Upper bound Maximal element theorem Existence of solution Applied mathematics |
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| References | Flores-Bazan (b6) 2003; 77 Lin, Yu, Ansari, Lai (b15) 2003; 284 Lin, Ansari (b12) 2004; 296 Petryshyn, Fitzpatrick (b16) 1974; 54 Repovs, Semenov (b17) 1998 Göfert, Tammer, Riahi, Zaˇlinescu (b7) 2003 Lin, Park (b13) 1998; 224 Ansari, Yao (b3) 2000; 76 Ansari, Wong, Yao (b2) 1999; 12 Lin, Park, Yu (b14) 1999; 233 Bianch, Schaible (b4) 1996; 90 Ansari, Idzik, Yao (b1) 2000; 15 Isac, Sehgal, Singh (b9) 1999; 41 Yuan (b19) 1999 Yuan, Isac, Tan, Yu (b20) 1998; 54 Hadjisavvas, Schaible (b8) 1998; 96 Chadli, Chiang, Yao (b5) 2002; 15 Wu, Shen (b18) 1996; 196 Li (b11) 2000; 13 Lan, Webb (b10) 1998; 126 Bianch (10.1016/j.aml.2006.04.016_b4) 1996; 90 Li (10.1016/j.aml.2006.04.016_b11) 2000; 13 Lin (10.1016/j.aml.2006.04.016_b14) 1999; 233 Yuan (10.1016/j.aml.2006.04.016_b20) 1998; 54 Ansari (10.1016/j.aml.2006.04.016_b3) 2000; 76 Göfert (10.1016/j.aml.2006.04.016_b7) 2003 Petryshyn (10.1016/j.aml.2006.04.016_b16) 1974; 54 Yuan (10.1016/j.aml.2006.04.016_b19) 1999 Ansari (10.1016/j.aml.2006.04.016_b1) 2000; 15 Ansari (10.1016/j.aml.2006.04.016_b2) 1999; 12 Lin (10.1016/j.aml.2006.04.016_b13) 1998; 224 Chadli (10.1016/j.aml.2006.04.016_b5) 2002; 15 Lan (10.1016/j.aml.2006.04.016_b10) 1998; 126 Lin (10.1016/j.aml.2006.04.016_b12) 2004; 296 Isac (10.1016/j.aml.2006.04.016_b9) 1999; 41 Lin (10.1016/j.aml.2006.04.016_b15) 2003; 284 Wu (10.1016/j.aml.2006.04.016_b18) 1996; 196 Repovs (10.1016/j.aml.2006.04.016_b17) 1998 Flores-Bazan (10.1016/j.aml.2006.04.016_b6) 2003; 77 Hadjisavvas (10.1016/j.aml.2006.04.016_b8) 1998; 96 |
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Appl. doi: 10.1006/jmaa.1996.0007 contributor: fullname: Wu – volume: 15 start-page: 327 year: 2002 ident: 10.1016/j.aml.2006.04.016_b5 article-title: Equilibrium problems with lower and upper bounds publication-title: Appl. Math. Lett. doi: 10.1016/S0893-9659(01)00139-2 contributor: fullname: Chadli – volume: 54 start-page: 135 year: 1998 ident: 10.1016/j.aml.2006.04.016_b20 article-title: The study of minimax inequalities, abstract economics and applications to variational inequalities and Nash equilibria publication-title: Acta Appl. Math. doi: 10.1023/A:1006095413166 contributor: fullname: Yuan – volume: 126 start-page: 1127 year: 1998 ident: 10.1016/j.aml.2006.04.016_b10 article-title: New fixed point theorems for a family of mappings and applications to problems on sets with convex sections publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-98-04347-0 contributor: fullname: Lan |
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| SubjectTerms | Exact sciences and technology Global analysis, analysis on manifolds Lower and upper bounds Mathematics Maximal element theorems Sciences and techniques of general use System of generalized implicit quasi-equilibrium problems System of quasi-equilibrium problems Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| Title | Systems of quasi-equilibrium problems with lower and upper bounds |
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