We consider the James and Schäffer type constants recently introduced by Takahashi. We prove an equality between James (resp. Schäffer) type constants and the modulus of convexity (resp. smoothness). By using these equalities, we obtain some estimates for the new constants in terms of the James constant. As a result, we improve an inequality between the Zbăganu and James constants.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-5,
author = {Fenghui Wang and Changsen Yang},
title = {An inequality between the James and James type constants in Banach spaces},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {191-201},
zbl = {1208.46019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-5}
}
Fenghui Wang; Changsen Yang. An inequality between the James and James type constants in Banach spaces. Studia Mathematica, Tome 196 (2010) pp. 191-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm201-2-5/