Lin, Y. Joseph and Tian, Guoqiang (1993): Minimax inequality equivalent to the FanKnasterKuratowskiMazurkiewicz Theorem. Published in: Applied Mathematics and Optimization , Vol. 28, (1993): pp. 173179.

PDF
MPRA_paper_41220.pdf Download (333kB)  Preview 
Abstract
The purpose of this note is to give further generalizations of the Ky Fan minimax inequality by relaxing the compactness and convexity of sets and the quasiconcavity of the functional and to show that our minimax inequalities are equivalent to the FanKnasterKuratowskiMazurkiewicz (FKKM) theorem and a modified FKKM theorem given in this note.
Item Type:  MPRA Paper 

Original Title:  Minimax inequality equivalent to the FanKnasterKuratowskiMazurkiewicz Theorem 
Language:  English 
Keywords:  The minimax inequality, Variational inequalities, The FKKM theorem, Noncompact and nonconvex sets, Equivalence 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement 
Item ID:  41220 
Depositing User:  Guoqiang Tian 
Date Deposited:  13. Sep 2012 22:47 
Last Modified:  16. Feb 2013 14:06 
References:  1. Allen G (1977) Variational inequalities, complementarity problems, and duality theorems. J Math Anal Appl 58:110 2. Aubin JP (1979) Mathematical Methods of Game and Economic Theory. NorthHolland, Amsterdam 3. Aubin JP, Ekeland I (1984) Applied Nonlinear Analysis. Wiley, New York 4. BenElMechaickh H, Deguire P, Granas A (1982) Points fixes et coincidences pour les applications multivoques (applications de Ky Fan). C R Acad Sci Paris S6r I Math 295:337340 5. BenEIMechaickh H, Deguire P, Granas A (1982) Points fixes et coincidences pour les fonctions multivoques II (applications de type q~ et q~). C R Acad Sci Paris Ser I Math 295:381384 6. Border KC (1985) Fixed Point Theorems with Applications to Economics and Game Theory. Cambridge University press, Cambridge 7. Fan K (1969) Extensions of two fixed point theorems of F. E. Browder. Math Z 112:234240 8. Fan K (1972) A minimax inequality and application. In: Inequalities, vol 3 (Shisha O, ed). Academic Press, New York, pp 103113 9. Fan K (1979) Fixedpoint and related theorems for noncompact sets. In: Game Theory and Related Topics (Moeschlin O, Pallaschke D, eds). NorthHolland, Amsterdam, pp 151156 10. Fan K (1984) Some properties of convex sets related to fixed points theorems. Math Ann 266:519537 11, Hartman PT, Stampacchia G (1966) On some nonlinear ecliptic differential functionalequations. Acta Math 115:153188 12. Knaster B, Kuratowski C, Mazurkiewicz S (1929) Ein Beweis des Fixpunktsatzes fiir ndemensionale Simpliexe. Fund Math 14:132137 13. Lassonde M (1983) On the use of KKM multifunctions in fixed point theory and related topics. J Math Anal Appl 97:151201 14. Mosco U (1976) Implicit variational problems and quasivariational inequalities. Lecture Notes in Mathematics, vol 543. SpringerVerlag, Berlin, pp 83156 15. Tarafdar E (1987) A fixed point theorem equivalent to the FanKnasterKuratowskiMazurkiewicz theorem. J Math Anal Appl 128:475479 16. Tian G (1991) Fixed points theorems for mappings with noncompact and nonconvex domains. J Math Anal Appl 158:160167 17. Tian G (1992) Existence of equilibrium in abstract economies with discontinuous payoffs and noncompact choice spaces. J Math Econom 21:379388 18. Tian G, Zhou J (1991) Quasivariational inequalities with noncompact sets.J Math Anal Appl 160:583595 19. Zhou J, Chen G (1988) Diagonal convexity conditions for problems in convex analysis and quasivariational inequalities. J Math Anal Appl 132:213225 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/41220 