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Existence Results for Set-Valued Vector Quasiequilibrium Problems

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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 2Y×2Y and A:E×K→2K,B:E×K→2E,F:E×K×K→2Y, C:E×K×K→2Y 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.

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Authors and Affiliations

  1. Institute of Mathematics, Hanoi, Vietnam

    P. H. Sach

  2. Ninh Thuan College of Pedagogy, Ninh Thuan, Vietnam

    L. A. Tuan

Authors
  1. P. H. Sach
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  2. L. A. Tuan
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Correspondence to P. H. Sach.

Additional information

Communicated by H.P. Benson.

The authors are indebted to the referees for valuable remarks.

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Sach, P.H., Tuan, L.A. Existence Results for Set-Valued Vector Quasiequilibrium Problems. J Optim Theory Appl 133, 229–240 (2007). https://doi.org/10.1007/s10957-007-9174-4

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  • DOI: https://doi.org/10.1007/s10957-007-9174-4

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