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Vectorial form of Ekeland-type variational principle with applications to vector equilibrium problems and fixed point theory. (English) Zbl 1127.49015
Summary: This paper introduces a vectorial form of equilibrium version of Ekeland-type variational principle. Some equivalent results to our variational principle are given. As applications, we derive the existence of solutions of a vector equilibrium problem in the setting of complete quasi-metric spaces with a $W$-distance. Caristi-Kirk fixed point theorem for multivalued maps is also established in a more general setting.

##### MSC:
 49J53 Set-valued and variational analysis 49J27 Optimal control problems in abstract spaces (existence) 47H10 Fixed-point theorems for nonlinear operators on topological linear spaces
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##### References:
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