On the vectorial Ekelandʹs variational principle and minimal points in product spaces Original Research Article

Phelps [13] noticed that the (scalar) Ekelandʹs variational principle (EVP) is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order. Attouch and Riahi [1] showed that EVP is equivalent to the existence of maximal points with respect to cones satisfying some additional conditions. Taking these into account, Göpfert and Tammer ([6], [7]) established a maximal point theorem in a product space. The aim of this paper is to obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial EVP.