On some consequences of Mazur-Orlicz theorem to Hahn-Banach-Lagrange theorem

摘要

The paper examines different kinds of p-convexity of a function g which are sufficient for the existence of a linear functional l p such that infA[ f + l. g] = infA[ f + p. g] 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 R with Dedekind vector lattice and present pf -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.