Journal of Optimization Theory and Applications

, Volume 90, Issue 1, pp 31–43

Generalized monotone bifunctions and equilibrium problems

  • M. Bianchi
  • S. Schaible
Contributed Papers

DOI: 10.1007/BF02192244

Cite this article as:
Bianchi, M. & Schaible, S. J Optim Theory Appl (1996) 90: 31. doi:10.1007/BF02192244


Using quasimonotone and pseudomonotone bifunctions, we derive existence results for the following equilibrium problem: given a closed and convex subsetK of a real topological vector space, find\(\bar x \in K\) such that\(F(\bar x,y) \geqslant 0\) for allyK. In addtion, we study the solution set and the uniquencess of a solution. The paper generalizes results obtained recently for variational inequalities.

Key Words

Generalized monotonicityequilibrium problemsvariational inequality problemsexistence of solutionsuniqueness

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • M. Bianchi
    • 1
  • S. Schaible
    • 2
  1. 1.Insitute of Econometrics and Mathematics for Economic DecisionsUniversitá CattolicaMilanItaly
  2. 2.Graduate School of ManagementUniversity of CalifornaiaRiverside