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Sullivan.t.j (talk | contribs) ←Created page with 'In mathematics, the '''modulus and characteristic of convexity''' are measures of "how convex" the unit ball in a Banach space is. In som...' |
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* The modulus of convexity, ''δ''(''ε''), is a [[monotonic function|non-decreasing]] and [[convex function]] of ''ε''.
* (''X'', || ||) is a [[uniformly convex space]] [[if and only if]] its characteristic of convexity ''ε''<sub>0</sub> = 0.
* (''X'', || ||) is a [[strictly convex space]] (i.e., the boundary of the unit ball ''B'' contains no line segments) if and only if ''δ''(2) = 1.
==Reference==
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