To each 
,
there corresponds a 
such that 
whenever 
and 
.
This is a geometric property of the unit sphere of
space: if the midpoint of a line
segment with endpoints on the surface of the sphere approaches the surface, then
the endpoints must come closer together (Cheney 1999).
Uniform Convexity
This entry contributed by Ronald M. Aarts
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References
Cheney, E. W. Introduction to Approximation Theory, 2nd ed. Providence, RI: Amer. Math. Soc., 1999.Referenced on Wolfram|Alpha
Uniform ConvexityCite this as:
Aarts, Ronald M. "Uniform Convexity." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/UniformConvexity.html