• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.697-709
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• 2001

Generalized forms of the von neumann-Sion type minimax theorem, the Fan-Ma intersection theorem, the Fan-a type analytic alternative, and the Nash-Ma equilibrium theorem hold for generalized convex spaces without having any linear structure.

• East Asian mathematical journal
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• v.25 no.4
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• pp.505-516
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• 2009

In this paper, we consider a new class of generalized mixed vector equilibrium-like problems in Banach spaces. By using Fan-KKM Theorem and Nadler's Theorem, we prove the existence theorem of solution for this class of generalized mixed vector equilibrium-like problems.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1297-1310
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• 2008

Main purpose of this paper is to combine the optimal form of Fan's best approximation theorem and Nash's equilibrium existence theorem into a single existence theorem simultaneously. For this, we first prove a general best proximity pair theorem which includes a number of known best proximity theorems. Next, we will introduce a new equilibrium concept for a generalized Nash game with normal form, and as applications, we will prove new existence theorems of Nash equilibrium pairs for generalized Nash games with normal form.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.29-35
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• 2010

In this note, we will prove a new equilibrium existence theorem for a compact acyclic strategic game by using Begle's fixed point theorem.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.301-307
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• 2003

The purpose of this paper is to give a generalization of the quasi fixed-point theorem due to Lefebvre, and prove a new existence theorem of equilibrium in a generalized quasi-game.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.425-430
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• 2012

In this paper, we will prove a social equilibrium existence theorem of a generalized Nash game with affine constraint correspondences which is comparable with Nash's equilibrium existence theorem in several aspects.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.932-944
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• 1998

In this paper we first prove a new minimum theorem using the upper semicontinuity of minimizing functions, which is comparable to Berge's theorem. Next, as applications, we shall prove the existence of equilibrium in generalized games and the existence theorem of zeros.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.19-26
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• 2006

In this paper, using the fixed point theorem for acyclic factorizable multifunctions, we shall prove an existence theorem of general best proximity pairs and equilibrium pairs for free generalized games.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.367-377
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• 2014

In this paper, we first introduce a generalized concept of Berge strong equilibrium for a generalized game $\mathcal{G}=(X_i;T_i,f_i)_{i{\in}I}$ of normal form, and using a fixed point theorem for compact acyclic maps in admissible convex sets, we establish the existence theorem of generalized Berge strong equilibrium for the game $\mathcal{G}$ with acyclic values. Also, we have demonstrated by examples that our new approach is useful to produce generalized Berge strong equilibria.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.1-28
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• 2000

In the present paper, we introduce fundamental results in the KKM theory for G-convex spaces which are equivalent to the Brouwer theorem, the Sperner lemma, and the KKM theorem. Those results are all abstract versions of known corresponding ones for convex subsets of topological vector spaces. Some earlier applications of those results are indicated. Finally, We give a new proof of the Himmelberg fixed point theorem and G-convex space versions of the von Neumann type minimax theorem and the Nash equilibrium theorem as typical examples of applications of our theory.