Fixed points, intersection theorems, variational inequalities, and equilibrium theorems
From a fixed point theorem for compact acyclic maps defined on admissible convex sets in the sense of Klee, we first deduce collectively fixed point theorems, intersection theorems for sets with convex sections, and quasi-equilibrium theorems. These quasi-equilibrium theorems are applied to give sim...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200002593 |
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| Summary: | From a fixed point theorem for compact acyclic maps defined on
admissible convex sets in the sense of Klee, we first deduce
collectively fixed point theorems, intersection theorems for sets
with convex sections, and quasi-equilibrium theorems. These
quasi-equilibrium theorems are applied to give simple and unified
proofs of the known variational inequalities of the
Hartman-Stampacchia-Browder type. Moreover, from our new fixed
point theorem, we deduce new variational inequalities which can be
used to obtain fixed point results for convex-valued maps.
Finally, various general economic equilibrium theorems are deduced
in the forms of the Nash type, the Tarafdar type, and the
Yannelis-Prabhakar type. Our results are stated for
not-necessarily locally convex topological vector spaces and for
abstract economies with arbitrary number of commodities and
agents. Our new results extend a lot of known works with much
simpler proofs. |
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| ISSN: | 0161-1712 1687-0425 |