An induction theorem and Ekeland's variational principle in partial metric spaces with applications. (2nd August 2020) - Hai, Le Phuoc; Khanh, Phan Quoc
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.