Original Articles

On Moduli of Convexity in Banach Spaces

Published in: Quaestiones Mathematicae
Volume 27 , issue 2 , 2004 , pages: 137–145

DOI: 10.2989/16073600409486089

Author(s): Diómedes Bárcenas , Vladimir Gurariy , Luisa Sánchez , Antonio Ullán

Keywords: MODULUS OF CONVEXITY

Abstract

We provide an example to show that the moduli of convexity δ_E and β_E are different. Our example allows us to prove that 2 is the best possible constant in the inequality δ_E ≤ β _E ≤ 2 δ _E and that β_E does not need to be a convex function.

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