Existence Results for Set-Valued Vector Quasiequilibrium Problems

P. H. Sach () and L. A. Tuan
Additional contact information
P. H. Sach: Institute of Mathematics
L. A. Tuan: Ninh Thuan College of Pedagogy

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 2, No 7, 229-240

Abstract: 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.

Keywords: Vector quasiequilibrium problems; Set-valued maps; Existence theorems; Diagonal quasiconvexity (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-007-9174-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:133:y:2007:i:2:d:10.1007_s10957-007-9174-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-007-9174-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().