An induction theorem and Ekeland's variational principle in partial metric spaces with applications. (2nd August 2020)

• Record Type: Journal Article
• Authors: Hai, Le Phuoc; Khanh, Phan Quoc
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1481
• Page End: 1511
• Publication Date: 2020-08-02
• Subjects: Partial metric spaces -- induction theorem -- the Ekeland variational principle -- minimizers and sharp minimizers -- fixed-point theorems; 90K26 -- 49J53 -- 90B48; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1589468
• Languages: English
• ISSNs: 0233-1934

Abstract

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.