Existence of Equilibria for Multivalued Mappings and Its Application to Vectorial Equilibria
- Cite this article as:
- Lin, L.J., Yu, Z.T. & Kassay, G. Journal of Optimization Theory and Applications (2002) 114: 189. doi:10.1023/A:1015420322818
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In this paper, we apply a new fixed-point theorem and use various monotonicity and some coercivity conditions to establish equilibrium theorems for multimaps. As a simple consequence, we give a unified approach to vectorial equilibria for multimaps. We show that, from our results, some well-known classical results, such as the Ky Fan minimax inequality theorem and the Browder and Hartman-Stampacchia theorems concerning the existence for variational inequalities, can be derived easily.