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Existence Results for Set-Valued Vector Quasiequilibrium Problems

  • P. H. SachEmail author
  • L. A. Tuan
Article

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 0A(z 0,x 0), and, for all ηA(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.

Keywords

Vector quasiequilibrium problems Set-valued maps Existence theorems Diagonal quasiconvexity 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Ninh Thuan College of PedagogyNinh ThuanVietnam

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