An induction theorem and Ekeland's variational principle in partial metric spaces with applications

Abstract

We prove an induction theorem and versions of the Ekeland variational principle for functions on partial metric spaces. As the distance is a partial metric, these versions have additional terms in comparison with the original principle. We also relax the usual lower semincontinuity assumption. Selected applications are provided: in conditions for the existence of solutions of noncompact nonconvex minimization problems, equilibrium problems, minimax equalities, in a particular model of minimization with sharp solutions together with an explicit expression of the sharpness, and in fixed-point studies.