GENERALIZED VECTOR QUASIVARIATIONAL-LIKE INEQUALITIES

  • KANG, MEE-KWANG (Department of Mathematics, Dongeui University) ;
  • LEE, BYUNG-SOO (Department of Mathematics, Kyungsung University)
  • Received : 2004.07.01
  • Published : 2004.12.25

Abstract

In this paper, we introduce two kinds of generalized vector quasivariational-like inequalities for multivalued mappings and show the existence of solutions to those variational inequalities under compact and non-compact assumptions, respectively.

Keywords

Multivalued mapping;vector quasivariational-like inequality;Ky Fan's Section Theorem;convex cone;upper semi-continuous

References

  1. J. Opti. Th. Appl. v.79 Generalized convex functions and vector variational inequalities Yang, X.Q.
  2. J. Math. Econ. v.12 Existence of maximal elements and equilibria in linear topological spaces Yannelis, N.C.;Prabhakar, N.D.
  3. J. Opti. Th. Appl. v.14 Cone convexity, cone extreme points and nondominated solutions in decision problems with multiobjectives Yu, P.L.
  4. J. Opti. Th. Appl. v.84 On vector variational inequalities Siddiqi, A.H.;Ansari, Q.H.;Khaliq. A.
  5. Nonlinear Anal. TMA v.21 Vector variational inequality and its duality Yang, X.Q.
  6. Lecture Notes in Econ. and Mathem. Systems v.319 Theory of Vector Optimization Luc, D.C.
  7. Appl. Math. Lett. v.1 General variational inequality Noor, M.A.
  8. Numer. Funct. Anal. & Optimiz. v.15 A unified approach to generalizations of the KKM-type theorems related to acyclic maps Park, S.
  9. Indian J. pure appl. Math. v.28 On Vector Variational-like inequalities Siddiqi, A.H.;Ansari, Q.H.;Ahmad, R.
  10. Appl. Math. Lett. v.6 Generalized vector variational inequality and fuzzy extension Lee, G.M.;Kim, D.S.;Lee, B.S.;Cho, S.J
  11. J. Math. Anal. Appl. v.203 On vector quasivariational inequalities Lee, G.M.;Lee, B.S.;Chang, S.S.
  12. J. of the Faculty of Sciences, Univ. of Tokyo, Section lA, Mathematics v.37 A special variational inequality and the implicit complementarity problem Isac, G.
  13. Nonlinear Analysis Forum v.8 Generalized nonlinear vector quasi variational-like inequalities Khaliq, A.
  14. Optimization v.46 On generalized vector quasi-variational inequalities Kim, W.K.;Tan, K.K.
  15. Indian J. pure appl. Math. v.28 Generalized vector variational-like inequalities on locally convex Hausdorff topologtcal vector spaces Lee, B.S.;Lee, G.M.;Kim, D.S.
  16. Theorems of alternative, quadratic programs, and complementarity problems, Variational Inequalities and Complementarity Problems Giannessi, F.;Cottle(ed.);Giannessi(ed.);Lions(ed.)
  17. Vector Variational Inequality and Vector Equilibria, Mathematical Theories Giannessi, F.
  18. Acta Mathematica v.115 On some nonlinear elliptic differential functional equations Hartman, P.;Stampacchia, G.
  19. Lecture Notes in Economics and Math. Systems v.285 Vector variational inequalitIes and vector optimization Chen, G.Y.;Cheng, G.M.
  20. Zeitscrift fur Operations Research v.3 A vector variational inequality and optimization over an efficient set Chen, G.Y.;Craven, B.D.
  21. J. Math. Anal. Appl. v.153 The vector complementarity problem and its equivalences with the weak minimal element in ordered spaces Chen, G.Y.;Yang, X.Q.
  22. J. Opti. Th. Appl. v.75 Pseudo-monotone complementarity problems in Hilbert spaces Cottle, R.W.;Yao, J.C.
  23. Mathematische Annalen v.142 A generalization of Tychonoff's fixed-point theorem Fan, Ky.
  24. Optimization v.41 A note on generalized vector variational-like inequalities Ansari, Q.H.
  25. Comput. Math. Appl. v.37 The existence theorems of solutions for generalized vector-valued variational-like inequalities Chang, S.S.;Thompson, H.B.;Yuan, G.X.Z.
  26. J. Opti. Th. Appl. v.74 Existence of solution for a vector variational inequality: An extension of the Hartman-Stampacchia theorem Chen, G.Y.
  27. Mathematische Nachrichten v.122 Quasi-variational inequalities in topological linear locally convex Hausdorff spaces Tan, N.X.