Tian, Guoqiang (1989): Fixed Points Theorems for Mappings with Non-compact and Non-Convex Domains. Published in: Journal of Mathematical Analysis and Applications , Vol. 158, (1991): pp. 161-167.
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This note gives some fixed point theorems for lower and upper semi-continuous mappings and mappings with open lower sections defined on non-compact and non-convex sets. It will be noted that the conditions of our theorems are not only sufficient but also necessary. Also our theorems generalize some well-known fixed point theorems such as the Kakutani fixed point theorem and the Brouwer-Schauder fixed point theorem by relaxing the compactness and convexity conditions.
|Item Type:||MPRA Paper|
|Original Title:||Fixed Points Theorems for Mappings with Non-compact and Non-Convex Domains|
|Keywords:||Fixed Points Theorems;Non-compact;Non-Convex; Domains|
|Subjects:||D - Microeconomics > D5 - General Equilibrium and Disequilibrium|
|Depositing User:||Guoqiang Tian|
|Date Deposited:||19. Sep 2012 11:40|
|Last Modified:||22. Aug 2015 00:40|
K. Arrow and G. Debreu, Existence of equilibrium for a competitive economy, Econometrica 22 (1954), 265-290.
J.P. Aubin, “Mathematical Methods of Game and Economic Theory,” North-Holland, Amsterdam, 1979.
J.P. Aubin and I. Ekeland, “Applied Nonlinear Analysis,” Wiley, New York, 1984.
K. C. BORBER, "Fixed Point Theorems with Application to Economics and Game Theory" Cambridge University Press, London, 1985.
F. E. Browder, Fixed point theorem for multivalued mappings in topological vector spaces, Math. Ann. 177 (1968), 283-301.
G. Debreu, A social equilibrium existence theorem, Proc. Natl. Acad. Sci. U.S.A. 38 (1952).
K. Fan, Extensions of two fixed points theorems of F. E. Browder, Math. Z. 112 (1969), 234-240.
B. Halpern, "Fixed piont theorems for outward maps," Doctoral Thesis, U.C. L. A., 1965.
J. Nash, Equilibrium points in N-person games, Proc. Natl. Acad. Sci. U.S.A. 36 (1950), 48-49.
G. Tian, Equilibrium in abstract economies with a non-compact infinite dimensional strategy space, an infinite number of agents and without ordered preferences, Econom. Lett., 33, 1990. 203-206.