Existence of equilibria for multivalued mapping and its application to vectorial equilibria

  • Authors:

  • L. J. Lin;Z. T. Yu;G. Kassay

  • Affiliations:

  • Professor, Department of Mathematics, National Changhua University of Education, Changhua, Taiwan, ROC;Associate Professor, Department of Electrical Engineering, Nan-Kai College, Nantour, Taiwan, ROC;Associate Professor, Department of Analysis and Optimization, Babes-Bolyai University, Cluj, Romania

  • Venue:
  • Journal of Optimization Theory and Applications
  • Year:
  • 2002

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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.