A GENERALIZED MINIMAX INEQUALITY RELATED TO ADMISSIBLE MULTIMAPS AND ITS APPLICATIONS

  • Park, Seh-Ie (Department of Mathematics Seoul National University)
  • 발행 : 1997.08.01

초록

From a minimax inequality related to admissible multimaps, we deduce generalized versions of lopsided saddle point theorems, fixed point theorems, existence of maximizable linear functionals, the Walras excess demand theorem, and the Gale-Nikaido-Debreu theorem.

키워드

참고문헌

  1. Mathematical Methods of Game and Economic Theory, (Rev. Ed.) J.­P. Aubin
  2. Proc. Amer. Math. Soc. v.122 A Leray-Schauder type theorem for approximable maps H. Ben-El-Mechaiekh;A. Idzik,
  3. Proc. Nat. Acad. Sci. USA v.74 On a sharpened form of the Schauder fixed point theorem F. E. Browder
  4. J. Math. Anal. Appl. v.159 Generalized KKM theorem and variational inequalities S.-S. Chang;Y. Zhang
  5. Convex Sets and Their Applications Ky, Fan
  6. Math. Z. v.112 Extensions of two fixed point theorems of F. E. Browder Ky, Fan
  7. Inequalities III A minimax inequality and applications Ky, Fan;O. Shisha(ed.)
  8. J. Math. pures et appl. v.65 Coincidences for set-valued maps and minimax inequalities A. Granas;F.­C. Liu
  9. Nonlinear Analysis v.5 On fixed points and variational inequalities - a circular tour J. Gwinner
  10. Math. Ann. v.248 Minimax and fixed point theorems C. W. Ha
  11. J. Math. Anal. Appl. v.97 On the use of KKM multimaps in fixed point theory and related topics M. Lassonde
  12. Contemp. Math. Amer. Math. Soc. v.72 Fixed point theorems on compact convex sets in topological vector spaces Sehie Park
  13. Nonlinear Analysis v.24 Acyclic maps, minimax inequalities and fixed points Sehie Park
  14. J. Korean Math. Soc. v.30 Fixed point theory of multimaps in topological vector spaces, II Sehie Park
  15. J. Korean Math. Soc. v.31 Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps Sehie Park
  16. J. Optimiz. Th. Appl. v.95 Generalized equilibrium problems and generalized complementarity problems Sehie Park
  17. World Congress of Nonlinear Analysts ’96.Proceedings Coincidence theorems for the better admissible multimaps and their applications Sehie Park;V. Lakshimikantham(ed.)
  18. Nonlinear Anal. TMA A unified approach to variational inequalities on compact convex sets Sehie Park;M.­P. Chen
  19. Proc. Coll. Natur. Sci. v.18 Admissible classes of multimaps on generalized convex spaces Sehie Park;H. Kim
  20. Proc. Symp. Pure Math. Amer. Math. Soc. v.45 Two function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems, S. Simons
  21. Fixed Point Theorems Nonlinear Functional Analysis and its Applications, I E. Zeidler
  22. J. Math. Anal. Appl. v.132 Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities J. X. Zhou;G. Chen