• 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 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.