%0 Journal Article
%T On moduli of convexity in Banach spaces
%A Reif Ji£¿¨ª
%J Journal of Inequalities and Applications
%D 2005
%I Springer
%X Let be a normed linear space, an element of norm one, and and the local modulus of convexity of . We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open -neighbourhood of in onto a set containing the open -neighbourhood of in . It is known that . We prove that there is no universal constant such that , however, such a constant exists within the class of Hilbert spaces . If is a Hilbert space with , then .
%U http://www.journalofinequalitiesandapplications.com/content/2005/695306