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Mathematical Methods of Operations Research

, Volume 64, Issue 1, pp 17–31 | Cite as

On the Existence of Solutions of Quasi-equilibrium Problems with Constraints

  • N. B. Minh
  • N. X. TanEmail author
Original Article

Abstract

The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of some vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimization problems with constraints.

Keywords

Upper quasi-equilibrium problem Lower quasi-equilibrium problem α Quasi-optimization problems Vector optimization problem Quasi-equilibrium problems Diagonally quasiconvex functions Diagonally upper and lower (T,C)-quasiconvex multivalued mappings Upper and lower C- continuous multivalued mappings 

AMS Subject Classification

90C 90D 49J 

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References

  1. Berge C (1959) Espaces Topologiques et Fontions Multivoques. Dunod, ParisGoogle Scholar
  2. Blum E, Oettli W (1993) From optimization and variational inequalities to equilibrium problems. Math Stud 64:1–23Google Scholar
  3. Chan D, Pang JS (1982) The generalized quasi-variational inequality problem. Math Oper Res 7:211–222zbMATHMathSciNetCrossRefGoogle Scholar
  4. Fu JY (2000) Generalized vector quasi-equilibrium problems. Math Methods Oper Res 52:57–64zbMATHCrossRefMathSciNetGoogle Scholar
  5. Fan K (1972) A minimax inequality and application. In: Shisha O (eds) Inequalities III. Academic, New-York, pp. 33Google Scholar
  6. Gurraggio A, Tan NX (2002) On general vector quasi-optimization problems. Math Methods Oper Res 55:347–358CrossRefMathSciNetGoogle Scholar
  7. Lin LJ, Yu ZT, Kassay G (2002) Existence of equilibria for monotone multivalued mappings and its applications to vectorial equilibria. J Optim Theory Appl 114:189–208zbMATHCrossRefMathSciNetGoogle Scholar
  8. Luc DT (1989) Theory of vector optimization, Lectures Notes in economics and mathematical systems, vol. 319. Springer, Berlin Heidelberg NewyorkGoogle Scholar
  9. Luc DT, Tan NX (2004) Existence conditions in variational inclusions with constraints. Optimization 53(5,6):505–515zbMATHCrossRefMathSciNetGoogle Scholar
  10. Minh NB, Tan NX (2000) Some sufficient conditions for the existence of equilibrium points concerning multivalued mappings. Vietnam J Math 28:295–310zbMATHMathSciNetGoogle Scholar
  11. Parida J, Sen A (1987) A variational-like inequality for multifunctions with applications. J Math Anal Appl 124:73–81zbMATHCrossRefMathSciNetGoogle Scholar
  12. Park S (2000) Fixed points and quasi-equilibrium problems. Nonlinear operator theory. Math Comput Model 32:1297–1304zbMATHGoogle Scholar
  13. Tan NX (2006) On the existence of solutions of quasivariational inclusion problems (in press)Google Scholar
  14. Tan NX, Tinh PN (1998) On the existence of equilibrium points of vector functions. Numer Funct Anal Optim 19:141–156zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Hanoi University of CommerceHanoiVietnam
  2. 2.Institute of MathematicsHanoiVietnam

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