uniformly convex space
A normed space is uniformly convex iff ∀ϵ>0 there exists δ>0 that satisfies
for ∥x∥≤1 ∥y∥≤1 and ∥x-y∥>ϵ ⇒ ∥x+y2∥≤1-δ.
For example it is easily seen that the normed space (ℝ2,∥.∥2) is uniformly convex space.
Also Lp and lp spaces for 1<p<∞ are uniformly convex, see J.A. Clarkson, ”Uniformly convex spaces”, Trans. Amer. Math. Society, 40 (1936), 396-414.
Title | uniformly convex space |
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Canonical name | UniformlyConvexSpace |
Date of creation | 2013-03-22 15:13:11 |
Last modified on | 2013-03-22 15:13:11 |
Owner | georgiosl (7242) |
Last modified by | georgiosl (7242) |
Numerical id | 32 |
Author | georgiosl (7242) |
Entry type | Definition |
Classification | msc 46H05 |
Synonym | uniformly convex |