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Vectorial form of Ekeland variational principle with applications to vector equilibrium problems. (English) Zbl 1434.58004

This paper is devoted to the study of vector equilibrium problems in relationship with related variational principles. In the first part of the paper under review, the authors establish an Ekeland-type variational principle in the abstract setting of vector-valued bifunctions. A feature of this result is that no triangular inequality hypothesis for bifunctions is assumed. In the final part of this paper, this abstract result is applied in order to obtain some existence results for solutions of vector equilibrium problems and vector quasi-equilibrium problems.

MSC:

58E30 Variational principles in infinite-dimensional spaces
90C29 Multi-objective and goal programming
49J40 Variational inequalities
47J30 Variational methods involving nonlinear operators

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