Mathematical Methods of Operations Research

, Volume 46, Issue 2, pp 147–152 | Cite as

A generalization of vectorial equilibria

  • Q. H. Ansari
  • W. Oettli
  • D. Schläger
Article

Abstract

A generalized form of vectorial equilibria is proposed, and, using an abstract monotonicity condition, an existence result is demonstrated.

Key words

Equilibrium problem multivalued mapping pseudomonotone mapping 

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References

  1. [1]
    Ansari QH (1996) Vector equilibrium problems and vector variational inequalities. Preprint, Department of Mathematics, Aligarh Muslim University, AligarhGoogle Scholar
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    Berge C (1966) Espaces topologiques — Fonctions multivoques. Dunod, ParisGoogle Scholar
  3. [3]
    Bianchi M, Hadjisavvas N, Schaible S (1997) Vector equilibrium problems with generalized monotone bifunctions. Journal of Optimization Theory and Applications 92, 3, forthcomingGoogle Scholar
  4. [4]
    Blum E, Oettli W (1994) From optimization and variational inequalities to equilibrium problems. The Mathematics Student 63:123–145Google Scholar
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    Chen GY (1992) Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem. Journal of Optimization Theory and Applications 74:445–456Google Scholar
  6. [6]
    Oettli W A remark on vector-valued equilibria and generalized monotonicity. Acta Mathematica Vietnamica, to appearGoogle Scholar

Copyright information

© Physica-Verlag 1997

Authors and Affiliations

  • Q. H. Ansari
    • 1
  • W. Oettli
    • 2
  • D. Schläger
    • 2
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Lehrstuhl für Mathematik VIIUniversität MannheimMannheimGermany

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