Journal of the Korean Mathematical Society (대한수학회지)
- Volume 35 Issue 2
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- Pages.491-502
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- 1998
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
FIXED POINT THEOREMS ON GENERALIZED CONVEX SPACES
Abstract
We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.
Keywords
- generalized convex space;
- G-convex space;
- fixed point;
- H-space;
- multifunction;
- upper semicontinuous (u.s.c);
- star refinement;
- Z-type;
- type I;
- type II