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Gap functions and existence of solutions for a system of vector equilibrium problems. (English) Zbl 1146.49005
Summary: In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector equilibrium problems are proved.
49J40Variational methods including variational inequalities
47N10Applications of operator theory in optimization, convex analysis, programming, economics
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