Journal of Optimization Theory and Applications

, Volume 114, Issue 1, pp 189–208

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

  • L. J. Lin
  • Z. T. Yu
  • G. Kassay

DOI: 10.1023/A:1015420322818

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


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.

transfer open multimap vectorial equilibria Cx-quasiconvex-like mapping G-convex space upper semicontinuity minimax inequalities 

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • L. J. Lin
    • 1
  • Z. T. Yu
    • 2
  • G. Kassay
    • 3
  1. 1.Department of MathematicsNational Changhua University of EducationChanghuaTaiwan, ROC
  2. 2.Department of Electrical EngineeringNan-Kai CollegeNantourTaiwan, ROC
  3. 3.Department of Analysis and OptimizationBabes-Bolyai UniversityClujRomania

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