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On vector quasi-equilibrium problems with set-valued maps. (English) Zbl 1061.90099
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 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.

MSC:
90C29Multi-objective programming; goal programming
49J53Set-valued and variational analysis
49J40Variational methods including variational inequalities