Existence of vector equilibria via Ekeland's variational principle (Q1012945)

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.