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Existence of Equilibria for Multivalued Mappings and Its Application to Vectorial Equilibria

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, ROC

    L. J. Lin (Professor)

  2. Department of Electrical Engineering, Nan-Kai College, Nantour, Taiwan, ROC

    Z. T. Yu (Associate Professor)

  3. Department of Analysis and Optimization, Babes-Bolyai University, Cluj, Romania

    G. Kassay (Associate Professor)

Authors
  1. L. J. Lin
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  2. Z. T. Yu
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  3. G. Kassay
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Lin, L.J., Yu, Z.T. & Kassay, G. Existence of Equilibria for Multivalued Mappings and Its Application to Vectorial Equilibria. Journal of Optimization Theory and Applications 114, 189–208 (2002). https://doi.org/10.1023/A:1015420322818

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  • DOI: https://doi.org/10.1023/A:1015420322818

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