Open Access

On moduli of convexity in Banach spaces

Journal of Inequalities and Applications20052005:695306

DOI: 10.1155/JIA.2005.423

Received: 15 September 2003

Published: 31 August 2005

Abstract

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 .

Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia

Copyright

© Reif. 2005