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Existence Results for Set-Valued Vector Quasiequilibrium Problems

Author

Listed:
  • P. H. Sach

    (Institute of Mathematics)

  • L. A. Tuan

    (Ninh Thuan College of Pedagogy)

Abstract

This paper deals with the set-valued vector quasiequilibrium problem of finding a point (z 0,x 0) of a set E×K such that (z 0,x 0)∈B(z 0,x 0)×A(z 0,x 0), and, for all η∈A(z 0,x 0), $$(F(z_{0},x_{0},\eta),C(z_{0},x_{0},\eta))\in\alpha,$$ where α is a subset of 2 Y ×2 Y and A:E×K→2 K ,B:E×K→2 E ,F:E×K×K→2 Y , C:E×K×K→2 Y are set-valued maps, with Y is a topological vector space. Two existence theorems are proven under different assumptions. Correct results of [Hou, S.H., Yu, H., Chen, G.Y.: J. Optim. Theory Appl. 119, 485–498 (2003)] are obtained from a special case of one of these theorems.

Suggested Citation

  • P. H. Sach & L. A. Tuan, 2007. "Existence Results for Set-Valued Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 229-240, May.
    • Handle: RePEc:spr:joptap:v:133:y:2007:i:2:d:10.1007_s10957-007-9174-4
    DOI: 10.1007/s10957-007-9174-4
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    References listed on IDEAS

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    4. L. J. Lin & Z. T. Yu & G. Kassay, 2002. "Existence of Equilibria for Multivalued Mappings and Its Application to Vectorial Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 189-208, July.
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    Cited by:

    1. P. H. Sach, 2008. "On a Class of Generalized Vector Quasiequilibrium Problems with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 337-350, November.
    2. R. P. Agarwal & M. Balaj & D. O’Regan, 2012. "A Unifying Approach to Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 417-429, November.
    3. M. Balaj & L. J. Lin, 2013. "Existence Criteria for the Solutions of Two Types of Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 232-246, February.

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