uniformly convex space

A normed space is uniformly convex iff ϵ>0 there exists δ>0 that satisfies for x1 y1 and x-y>ϵ x+y21-δ.

For example it is easily seen that the normed space (2,.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
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