Araya, Yousuke; Kimura, Kenji; Tanaka, Tamaki Existence of vector equilibria via Ekeland’s variational principle. (English) Zbl 1172.65032 Taiwanese J. Math. 12, No. 8, 1991-2000 (2008). The authors use a nonlinear scalarizing function to the case of a vector-valued function leading to a variational principle for the vector equilibrium problem. Then the authors obtain a Caristi-Kirk type fixed point theorem and an existence result for the vector equilibrium problem. The paper generalizes the vectorial Caristi-Kirk fixed point theorem and the vectorial Takahashi’s nonconvex minimization theorem. Reviewer: Yves Cherruault (Paris) Cited in 7 Documents MSC: 65K10 Numerical optimization and variational techniques 58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc. 90C29 Multi-objective and goal programming Keywords:Ekeland’s variational principle; vector valued solution; approximate solution; vector equilibrium problem; Caristi-Kirk type fixed point theorem; Takahashi’s nonconvex minimization theorem PDFBibTeX XMLCite \textit{Y. Araya} et al., Taiwanese J. Math. 12, No. 8, 1991--2000 (2008; Zbl 1172.65032) Full Text: DOI