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In mathematics, a strictly convex space is a normed topological vector space (''V'', || ||) for which the unit ball is a strictly convex set. Put another way, a strictly convex space is one for which, given any two points ''x'' and ''y'' in the boundary ∂''B'' of the unit ball ''B'' of ''V'', the affine line ''L''(''x'', ''y'') passing through ''x'' and ''y'' meets ∂''B'' ''only'' at ''x'' and ''y''. Strict convexity is somewhere between an inner product space (all inner product spaces are strictly convex) and a general normed space (all strictly convex normed spaces are normed spaces) in terms of structure. It also guarantees the uniqueness of a best approximation to an element in ''X'' (strictly convex) out of ''Y'' (a subspace of ''X'') if indeed such an approximation exists. ==Properties== * A Banach space (''V'', || ||) is strictly convex if and only if the modulus of convexity ''δ'' for (''V'', || ||) satisfies ''δ''(2) = 1. * A Banach space (''V'', || ||) is strictly convex if and only if ''x'' ≠ ''y'' and || ''x'' || = || ''y'' || = 1 together imply that || ''x'' + ''y'' || < 2. * A Banach space (''V'', || ||) is strictly convex if and only if ''x'' ≠ ''y'' and || ''x'' || = || ''y'' || = 1 together imply that || ''αx'' + (1 − ''α'')''y'' || < 1 for all 0 < ''α'' < 1. * A Banach space (''V'', || ||) is strictly convex if and only if ''x'' ≠ ''0'' and ''y'' ≠ ''0'' and || ''x'' + ''y'' || = || ''x'' || + || ''y'' || together imply that ''x'' = ''cy'' for some constant ''c > 0''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Strictly convex space」の詳細全文を読む スポンサード リンク
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