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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-1-5,
author = {Fon-Che Liu},
title = {Mazur-Orlicz equality},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {53-63},
zbl = {1162.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-1-5}
}
Fon-Che Liu. Mazur-Orlicz equality. Studia Mathematica, Tome 187 (2008) pp. 53-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-1-5/