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Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities

Author

Listed:
  • O. Chaldi

    (University Cadi Ayyad)

  • Z. Chbani

    (University Cadi Ayyad)

  • H. Riahi

    (University Cadi Ayyad)

Abstract

This paper attempts to generalize and unify several new results that have been obtained in the ongoing research area of existence of solutions for equilibrium problems. First, we propose sufficient conditions, which include generalized monotonicity and weak coercivity conditions, for existence of equilibrium points. As consequences, we generalize various recent theorems on the existence of such solutions. For applications, we treat some generalized variational inequalities and complementarity problems. In addition, considering penalty functions, we study the position of a selected solution by relying on the viscosity principle.

Suggested Citation

  • O. Chaldi & Z. Chbani & H. Riahi, 2000. "Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 299-323, May.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:2:d:10.1023_a:1004657817758
    DOI: 10.1023/A:1004657817758
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    References listed on IDEAS

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    1. Romesh Saigal, 1976. "Extension of the Generalized Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 260-266, August.
    2. R. C. Riddell, 1981. "Equivalence of Nonlinear Complementarity Problems and Least Element Problems in Banach Lattices," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 462-474, August.
    3. Monica Bianchi, 1993. "Una classe di funzioni monotone generalizzate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 16(1), pages 17-32, March.
    4. Richard W. Cottle & Jong-Shi Pang, 1978. "A Least-Element Theory of Solving Linear Complementarity Problems as Linear Programs," Mathematics of Operations Research, INFORMS, vol. 3(2), pages 155-170, May.
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