Ekeland variational principles for vector equilibrium problems

Abstract

This work concerns Ekeland variational principles for scalar and vector cyclically antimonotone bifunctions on complete metric spaces. The scalar results work for extended bifunctions and they are obtained by a generalized version of the Dancs–Hegedüs–Medvegyev's fixed point theorem. As a result, weaker lower-semicontinuity assumptions have been considered, that generalize the concept of strictly decreasingly lower-semicontinuous real-valued function. The vector results are derived from the previous ones by a scalarization approach and are based on new notions of cyclical antimonotonicity, lower boundedness and strictly decreasingly lower-semicontinuity for vector bifunctions. Several results in the literature are improved since they are stated by weaker assumptions.