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

The paper examines different kinds of p-convexity of a function g which are sufficient for the existence of a linear functional <inline-graphic></inline-graphic> such that <inline-graphic></inline-graphic> 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 <inline-graphic></inline-graphic> with Dedekind vector lattice and present <inline-graphic></inline-graphic> -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. [ABSTRACT FROM AUTHOR]