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A variational principle for vector equilibrium problems. (English) Zbl 1019.49017

The author describes a variational principle for vector equilibrium problems of finding xK such that

f(x,y)-intP

for all yK, where intP denotes the topological interior of the cone P, X is a real topological vector space, K is a nonempty closed convex subset of X, (Y,P) is a real ordered topological vector space, and f:X×XY is a mapping with f(x,x)=0 for all xX. Under some conditions, the author analyses the solutions for vector equilibrium problems and obtains some new results.

MSC:
49J40Variational methods including variational inequalities
90C29Multi-objective programming; goal programming
91B52Special types of equilibria in economics
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