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),
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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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