Exact and approximate vector Ekeland variational principles

Abstract

This paper concerns with exact and approximate Ekeland variational principles for vector-valued functions and bifunctions that are derived via linear and nonlinear scalarization processes by an approximate scalar formulation of the Ekeland variational principle and a revised version of Dancs-Hegedüs-Medvegyev’s fixed point theorem. Both results are also interesting in themselves and involve really mild assumptions. As a result, the obtained Ekeland variational principles improve some recent results in the literature since weaker assumptions are required