Fixed points theorems for mappings with non-compact and non-convex domains
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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. 1991.
Journal of Mathematical Analysis and Applications
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