The Journal of the Indian Mathematical Society

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G-KKM Theorem on Non-Convex Sets and its Applications


Affiliations
1 Department of Mathematics Education, National Hsinchu Teacher’s College, Hsinchu, Taiwan, R.O.C, Taiwan, Province of China
     

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In this paper, we invoke non-convexity of constraint regions in place of convexity and we obtain the new fixed point theorem, “ Let X be an almost (7-convex subset (nearly C-convex Set) of a locally G-convex space E. If T ∈ G-KKM(X, X) is compact and closed, then it has a fixed point.”

Keywords

G-KKM Property, G-KKM Theorem, Matching Theorem, Fixed Point Theorem, Almost G-Convex, Nearly G-Convex.
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  • G-KKM Theorem on Non-Convex Sets and its Applications

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Authors

Chi-Ming Chen
Department of Mathematics Education, National Hsinchu Teacher’s College, Hsinchu, Taiwan, R.O.C, Taiwan, Province of China

Abstract


In this paper, we invoke non-convexity of constraint regions in place of convexity and we obtain the new fixed point theorem, “ Let X be an almost (7-convex subset (nearly C-convex Set) of a locally G-convex space E. If T ∈ G-KKM(X, X) is compact and closed, then it has a fixed point.”

Keywords


G-KKM Property, G-KKM Theorem, Matching Theorem, Fixed Point Theorem, Almost G-Convex, Nearly G-Convex.