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Vector Equilibrium Problems on Dense Sets

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  • Szilárd László

    (Technical University of Cluj-Napoca)

Abstract

In this paper, we provide sufficient conditions that ensure the existence of the solution of some vector equilibrium problems in Hausdorff topological vector spaces ordered by a cone. The conditions that we consider are imposed not on the whole domain of the operators involved, but rather on a self-segment-dense subset of it, a special type of dense subset. We apply the obtained results to vector optimization and vector variational inequalities.

Suggested Citation

  • Szilárd László, 2016. "Vector Equilibrium Problems on Dense Sets," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 437-457, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0915-0
    DOI: 10.1007/s10957-016-0915-0
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    References listed on IDEAS

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    1. Szilárd László & Adrian Viorel, 2015. "Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 52-75, July.
    2. Q. Ansari & W. Oettli & D. Schläger, 1997. "A generalization of vectorial equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 147-152, June.
    3. X. H. Gong, 2001. "Efficiency and Henig Efficiency for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 139-154, January.
    4. Q.H. Ansari & I.V. Konnov & J.C. Yao, 2002. "Characterizations of Solutions for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 435-447, June.
    5. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
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