On some consequences of Mazur–Orlicz theorem to Hahn–Banach–Lagrange theorem. (3rd July 2018)

• Record Type: Journal Article
• Authors: Grzybowski, Jerzy; Pallaschke, Diethard; Przybycień, Hubert; Urbański, Ryszard
• Is Part Of: Optimization. Volume 67:Number 7(2018)
• Page Start: 1005
• Page End: 1015
• Publication Date: 2018-07-03
• Subjects: Hahn–Banach–Lagrange theorem -- monotonicity -- convex analysis; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1295044
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The paper examines different kinds of p -convexity of a function g which are sufficient for the existence of a linear functional such that in Theorem 1.13 of Simons in his monograph 'From Hahn–Banach to monotonicity', published in Springer lecture notes (2008). We replace sublinearity of p with convexity, the field with Dedekind vector lattice and present -convexity which is also necessary. In Theorem 4.7 we also generalize a result of MM. Neumann from 1991 published in Czech. Mathem. Journal Vol 41 on the Mazur–Orlicz theorem.