On the vectorial Ekeland's variational principle and minimal points in product spaces

Phelps [13] noticed that the (scalar) Ekeland's 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, Gopfert 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. (C) 2000 Elsevier Science Ltd. All rights reserved.