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Vectorial form of Ekeland-type variational principle in locally convex spaces and its applications. (English) Zbl 1218.46047
Summary: By using Danes’s drop theorem in locally convex spaces, we obtain a vectorial form of the Ekeland-type variational principle in locally convex spaces. From this theorem, we derive some versions of a vectorial Caristi-Kirk fixed-point theorem, Takahashi’s nonconvex minimization theorem, and Oettli-Théra’s theorem. Furthermore, we show that these results are equivalent to each other. Also, the existence of solution of a vector equilibrium problem is given.
MSC:
46N10Applications of functional analysis in optimization and programming
46A03General theory of locally convex spaces
49J27Optimal control problems in abstract spaces (existence)
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