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On Moduli of Convexity in Banach Spaces
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 δE ≤
βE ≤ 2δE and that βE does not need to
be a convex
function.
Mathematics Subject Classification (2000): Primary 46B20, 46B50.
Key words: Modulus
of convexity.
Quaestiones Mathematicae 27(2004), 137-145.
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 δE ≤
βE ≤ 2δE and that βE does not need to
be a convex
function.
Mathematics Subject Classification (2000): Primary 46B20, 46B50.
Key words: Modulus
of convexity.
Quaestiones Mathematicae 27(2004), 137-145.
