Uniformly convex space

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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 there is some so that for any two vectors with and the condition

implies that:

Intuitively, the center of a line segment inside the unit ball must lie deep inside the unit ball unless the segment is short.



See also


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  • Lindenstrauss, Joram and Benyamini, Yoav. Geometric nonlinear functional analysis Colloquium publications, 48. American Mathematical Society.