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Reference.org
Modulus and characteristic of convexity
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the modulus of convexity and the characteristic of convexity are measures of "how <a href="/facts/Convex_set/vdAuJRJl">convex</a>" the <a href="/facts/Unit_ball/5UeoTcug">unit ball</a> in a <a href="/facts/Banach_space/sDEIk7EC">Banach space</a> is. In some sense, the modulus of convexity has the same relationship to the <i>ε</i>-<i>δ</i> definition of <a href="/facts/Uniformly_convex_space/H9gGXdy7">uniform convexity</a> as the <a href="/facts/Modulus_of_continuity/31lThXhW">modulus of continuity</a> does to the <i>ε</i>-<i>δ</i> definition of <a href="/facts/Continuous_function/sKbl02pB">continuity</a>. </p>