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Vietnam
Journal of Mathematics 37:4 (2009) 419-441
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Applications of Fixed Point Theorems for Acyclic
Maps -- A Review
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Sehie Park
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Abstract. We review applications of our fixed
point theorems on compact compositions of acyclic maps. Our applications
are mainly on acyclic polyhedra, locally convex topological vector spaces,
admissible (in the sense of Klee) convex sets, and almost convex or Klee
approximable sets in topological vector spaces. Those applications are
concerned with general equilibrium problems like as (collective) fixed
point theorems, the von Neumann type intersection theorems, the von Neumann
type minimax theorems, the Nash type equilibrium theorems, cyclic
coincidence theorems, best approximation theorems, (quasi-) variational
inequalities, and the Gale-Nikaido-Debreu theorem. Finally, we briefly
introduce some related results mainly appeared in other author's works.
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2000 Mathematics Subject Classification: 47H10, 49J53,
54C60, 54H25, 55M20, 90A14, 91A13.
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Keywords: Kakutani map, acyclic map, admissible set
(in the sense of Klee), equilibrium problems, von Neumann minimax theorem,
Nash equilibrium theorem.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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