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Zbl 1061.90099
Hou, S.H.; Yu, H.; Chen, G.Y.
On vector quasi-equilibrium problems with set-valued maps. (English)
[J] J. Optimization Theory Appl. 119, No. 3, 485-498 (2003). ISSN 0022-3239; ISSN 1573-2878/e

Summary: We introduce a new class of vector quasi-equilibrium problems with set-valued maps. Almost all the vector equilibrium models of the Blum-Oettli type in the literature are special cases of our new class of equilibrium problems under consideration. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the $\gamma$-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for such vector equilibrium problems.

MSC 2000:: *90C29 Multi-objective programming, etc.
49J53 Set-valued and variational analysis
49J40 Variational methods including variational inequalities

Keywords: Vector quasi-equilibrium problems; set-valued maps; lower sections; C-diagonal quasiconvexity; continuous selection; fixed points

Cited in: Zbl 1231.90379 Zbl 1144.49012 Zbl 1141.47045

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