Generalized strong vector quasi-equilibrium problem with domination structure
In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for stro...
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| Published in | Journal of global optimization Vol. 55; no. 4; pp. 839 - 847 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.04.2013
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0925-5001 1573-2916 |
| DOI | 10.1007/s10898-012-9889-0 |
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| Abstract | In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khan’s main results are corrected. |
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| AbstractList | In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khan's main results are corrected. In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khan's main results are corrected. Keywords Strong vector equilibrium problem * Domination structure * Cone-continuity * Fan-KKM theorem * Strong vector F-implicit variational inequality problem Mathematics Subject Classification 90C33 * 49J40 * 47H10 In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khanâ[euro](TM)s main results are corrected.[PUBLICATION ABSTRACT] |
| Audience | Academic |
| Author | Wang, Sanhua Fu, Junyi |
| Author_xml | – sequence: 1 givenname: Junyi surname: Fu fullname: Fu, Junyi email: fujunyihotmail@tom.com organization: Department of Mathematics, Nanchang University – sequence: 2 givenname: Sanhua surname: Wang fullname: Wang, Sanhua organization: Department of Mathematics, Nanchang University |
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| CitedBy_id | crossref_primary_10_1186_s13663_015_0277_6 crossref_primary_10_1007_s10957_014_0630_7 crossref_primary_10_1186_s13660_019_2063_1 crossref_primary_10_1007_s10957_018_1331_4 crossref_primary_10_1080_02331934_2018_1432607 |
| Cites_doi | 10.1016/S0362-546X(01)00199-7 10.1007/s10957-004-5726-z 10.1007/s11590-010-0192-z 10.1016/j.aml.2007.12.008 10.1016/j.mcm.2007.04.013 10.1016/j.aml.2005.07.003 10.1007/BFb0059130 10.1007/BF01458545 10.1007/s10898-003-2683-2 10.1007/978-0-387-77247-9 10.1007/978-1-4419-0158-3 10.1023/A:1022603406244 10.1007/s11590-010-0179-9 10.1007/s00186-006-0114-0 10.1007/s10898-007-9160-2 10.1007/s11590-007-0062-5 10.1002/mana.19851220123 10.1007/s10898-010-9557-1 10.1007/s001860000058 10.1007/s10957-010-9656-7 10.1016/j.jmaa.2008.01.026 10.1016/S0022-247X(02)00535-8 10.1016/j.aml.2006.05.010 |
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| DOI | 10.1007/s10898-012-9889-0 |
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| Keywords | Strong vector equilibrium problem Fan-KKM theorem 47H10 Strong vector F-implicit variational inequality problem 90C33 49J40 Domination structure Cone-continuity |
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Lett.2008234134910.1007/s11590-007-0062-5 LeeB.S.Firdosh KhanM.SalahuddinVector F-implicit complementarity problems with corresponding variational inequality problemsAppl. Math. Lett.20072043343810.1016/j.aml.2006.05.010 PengJ.W.WuS.Y.The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problemsOptim. Lett.2010450151210.1007/s11590-010-0179-9 TanN.X.On the existence of solutions of quasivariational inclusion problemsJ. Optim. Theory Appl.200412361963810.1007/s10957-004-5726-z GöpfertA.RiahiH.TammerC.ZălinescuC.Variational Methods in Partially Ordered Spaces2003New York, NY, USASpringer AubinJ.P.EkelandI.Applied Nonlinear Analysis1984New York, NY, USAWiley GongX.H.Symmetric strong vector quasi-equilibrium problemsMath. Meth. Oper. Res.20076530531410.1007/s00186-006-0114-0 LiJ.HuangN.J.Vector F-implicit complementarity problems in Banach spacesAppl. Math. 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| References_xml | – reference: FuJ.Y.Generalized vector quasi-equilibrium problemsMath. Meth. Oper. Res.200052576410.1007/s001860000058 – reference: GiannessiF.MaugeriA.PardalosP.M.Equilibrium Problems and Variational Models2001DordrechtKluwer – reference: AnsariQ.H.KonnovI.V.YaoJ.C.On generalized vector equilibrium problemsNonlinear Anal. TMA20014754355410.1016/S0362-546X(01)00199-7 – reference: FanK.Some properties of convex sets related to fixed point theoremsMath. Ann.198426651953710.1007/BF01458545 – reference: BergeC.Topological Spaces1963EdinburghOliver and Boyd Ltd – reference: ChenG.Y.YangX.Q.YuH.A nonlinear scalarization function and generalized quasivector equilibrium problemsJ. Global Optim.20053245146610.1007/s10898-003-2683-2 – reference: HouS.H.GongX.H.YangX.M.Existence and stability of solutions for generalized Ky Fan inequality problems with trifunctionsJ. Optim. Theory Appl.201014638739810.1007/s10957-010-9656-7 – reference: AubinJ.P.EkelandI.Applied Nonlinear Analysis1984New York, NY, USAWiley – reference: AnsariQ.H.Flores-BazanF.Generalized vector quasi-equilibrium problems with applicationsJ. Math. Anal. Appl.200327724625610.1016/S0022-247X(02)00535-8 – reference: GongX.H.Optimality conditions for vector equilibrium problemsJ. Math. Anal. Appl.20083421455146610.1016/j.jmaa.2008.01.026 – reference: Khan, S.A.: Generalized vector implicit quasi complementarity problems. J. Global Optim. doi:10.1007/s10898-010-9557-1 – reference: LucD.T.Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 3191989BerlinSpringer – reference: TanN.X.On the existence of solutions of quasivariational inclusion problemsJ. Optim. Theory Appl.200412361963810.1007/s10957-004-5726-z – reference: GiannessiF.Vector Variational Inequalities and Vector Equilibria: Mathematical Theories2000DordrechtKluwer – reference: LinL.J.WangS.Y.ChuangC.S.Existence theorems of systems of variational inclusion problems with applicationsJ. Global Optim.20084075176410.1007/s10898-007-9160-2 – reference: BianchiM.HadjisavvasN.SchaibleS.Vector equilibrium problems with generalized monotone bifunctionsJ. Optim. Theory Appl.19979252754210.1023/A:1022603406244 – reference: GöpfertA.RiahiH.TammerC.ZălinescuC.Variational Methods in Partially Ordered Spaces2003New York, NY, USASpringer – reference: BlumE.OettliW.From optimization and variational inequalities to equilibrium problemsMath. Stud.199463123145 – reference: JahnJ.Mathematical Vector Optimization in Partially Ordered Linear Spaces1986FrankfurtPeter Lang – reference: LiS.J.ZengJ.Existences of solutions for generalized vector quasi-equilibrium problemsOptim. Lett.2008234134910.1007/s11590-007-0062-5 – reference: ChenG.Y.HuangX.X.YangX.Q.Vector Optimization, Set-Valued and Variational Analysis2005BerlinSpringer – reference: LongX.J.HuangN.J.TeoK.L.Existence and stability of solutions for generalized vector quasi-equilibrium problemMath. Comput. Model.20084744545110.1016/j.mcm.2007.04.013 – reference: ChenC.R.LiS.J.ZengJ.LiX.B.Error analysis of approximate solutions to parametric vector quasiequilibrium problemsOptim. Lett.20115859810.1007/s11590-010-0192-z – reference: ChinchuluunA.MigdalasA.PardalosP.M.PitsoulisL.Pareto Optimality, Game Theory and Equilibria2008New YorkSpringer10.1007/978-0-387-77247-9 – reference: GongX.H.Symmetric strong vector quasi-equilibrium problemsMath. Meth. Oper. Res.20076530531410.1007/s00186-006-0114-0 – reference: PengJ.W.WuS.Y.The generalized Tykhonov well-posedness for system of vector quasi-equilibrium problemsOptim. 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| SubjectTerms | Computer Science Equilibrium Inequalities Inequality Mapping Mathematical analysis Mathematics Mathematics and Statistics Neighborhoods Operations Research/Decision Theory Optimization Real Functions Theorems Vectors (mathematics) |
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| Title | Generalized strong vector quasi-equilibrium problem with domination structure |
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