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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Caristi fixed-point theorem ： ウィキペディア英語版 Caristi fixed-point theorem In mathematics, the Caristi fixed-point theorem (also known as the Caristi–Kirk fixed-point theorem) generalizes the Banach fixed point theorem for maps of a complete metric space into itself. Caristi's fixed-point theorem is a variation of the ''ε''-variational principle of Ekeland (1974, 1979). Moreover, the conclusion of Caristi's theorem is equivalent to metric completeness, as proved by Weston (1977). The original result is due to the mathematicians James Caristi and William Arthur Kirk. ==Statement of the theorem== Let (''X'', ''d'') be a complete metric space. Let ''T'' : ''X'' → ''X'' and ''f'' : ''X'' → [0, +∞) be a lower semicontinuous function from ''X'' into the non-negative real numbers. Suppose that, for all points ''x'' in ''X'', :$d\; \backslash big(\; x,\; T(x)\; \backslash big)\; \backslash leq\; f(x)\; -\; f\; \backslash big(\; T(x)\; \backslash big).$ Then ''T'' has a fixed point in ''X'', i.e. a point ''x''0 such that ''T''(''x''0) = ''x''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「Caristi fixed-point theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.