On some consequences of Mazur–Orlicz theorem to Hahn–Banach–Lagrange theorem
| Autor: | Diethard Pallaschke, Ryszard Urbański, Jerzy Grzybowski, Hubert Przybycień |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Mathematics::Functional Analysis 021103 operations research Control and Optimization Applied Mathematics 0211 other engineering and technologies Hahn–Banach theorem Field (mathematics) Monotonic function 02 engineering and technology Management Science and Operations Research Lattice (discrete subgroup) 01 natural sciences Convexity 010101 applied mathematics Linear form Dedekind cut 0101 mathematics Carlson's theorem Mathematics |
| Zdroj: | Optimization. 67:1005-1015 |
| ISSN: | 1029-4945 0233-1934 |
| DOI: | 10.1080/02331934.2017.1295044 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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