We use one-dimensional differential inequalities to estimate the squareness and type of Banach spaces with modulus of convexity of power type two. The estimates obtained are sharp and the constants involved moderate.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-1-7, author = {M. Ivanov and A. J. Pallares and S. Troyanski}, title = {On the geometry of Banach spaces with modulus of convexity of power type 2}, journal = {Studia Mathematica}, volume = {196}, year = {2010}, pages = {81-91}, zbl = {1200.46013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-1-7} }
M. Ivanov; A. J. Pallares; S. Troyanski. On the geometry of Banach spaces with modulus of convexity of power type 2. Studia Mathematica, Tome 196 (2010) pp. 81-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-1-7/