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The Convergent Behavior for Parametric Generalized Vector Equilibrium Problems

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  • Yen-Cherng Lin
  • Po-Jen Cheng
  • Su-Ling Lee

Abstract

We study some properties for parametric generalized vector equilibrium problems and the convergent behavior for the correspondent solution sets of this problem under some suitable conditions. Several existence results and the topological structures of the efficient solutions set are established. Some new results of existence for weak solutions and strong solutions are derived. Finally, we give some examples to illustrate our theory including the example studied by Fang (1992), who established the perturbed nonlinear program (Pμ) and described successfully that the optimal solution of (Pμ) will approach the optimal solution of linear program (P).

Suggested Citation

  • Yen-Cherng Lin & Po-Jen Cheng & Su-Ling Lee, 2012. "The Convergent Behavior for Parametric Generalized Vector Equilibrium Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:183040
    DOI: 10.1155/2012/183040
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    References listed on IDEAS

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    1. Li, S.J. & Li, X.B. & Wang, L.N. & Teo, K.L., 2009. "The Hölder continuity of solutions to generalized vector equilibrium problems," European Journal of Operational Research, Elsevier, vol. 199(2), pages 334-338, December.
    2. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
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    Cited by:

    1. Qi-Qing Song, 2013. "The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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