On Vector Quasi-Equilibrium Problems with Set-Valued Maps

S. H. Hou, H. Yu and G. Y. Chen
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S. H. Hou: Hong Kong Polytechnic University
H. Yu: Institute of Systems Science
G. Y. Chen: Institute of Systems Science

Journal of Optimization Theory and Applications, 2003, vol. 119, issue 3, No 3, 485-498

Abstract: Abstract In this paper, 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 γ-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.

Keywords: Vector quasi-equilibrium problems; set-valued maps; lower sections; C-diagonal quasiconvexity; continuous selection; fixed points (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (8)

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DOI: 10.1023/B:JOTA.0000006686.19635.ad

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