Tom 189 / 2008
Studia Mathematica 189 (2008), 53-63 MSC: 46A20, 46A22. DOI: 10.4064/sm189-1-5
A remarkable theorem of Mazur and Orlicz which generalizes the Hahn–Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur–Orlicz equality. Applications of the Mazur–Orlicz equality to lower barycenters for means, separation principles, Lax–Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.