Fixed Points Theorems for Mappings with Non-compact and Non-Convex Domains
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.
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- Tian, Guoqiang, 1990. "Equilibrium in abstract economies with a non-compact infinite dimensional strategy space, an infinite number of agents and without ordered preferences," Economics Letters, Elsevier, vol. 33(3), pages 203-206, July.
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