Uniformly convex space

In mathematics, uniformly convex spaces (or uniformly rotund spaces) are common examples of reflexive Banach spaces. The concept of uniform convexity was first introduced by James A. Clarkson in 1936.

A uniformly convex space is a normed vector space so that, for every ${\displaystyle 0<\epsilon \leq 2}$ there is some ${\displaystyle \delta >0}$ so that for any two vectors with ${\displaystyle \|x\|=1}$ and ${\displaystyle \|y\|=1,}$ the condition

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