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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 Pseudo-monotone operator ： ウィキペディア英語版 Pseudo-monotone operator In mathematics, a pseudo-monotone operator from a reflexive Banach space into its continuous dual space is one that is, in some sense, almost as well-behaved as a monotone operator. Many problems in the calculus of variations can be expressed using operators that are pseudo-monotone, and pseudo-monotonicity in turn implies the existence of solutions to these problems. ==Definition== Let (''X'', || ||) be a reflexive Banach space. A map ''T'' : ''X'' → ''X''∗ from ''X'' into its continuous dual space ''X''∗ is said to be pseudo-monotone if ''T'' is a bounded operator (not necessarily continuous) and if whenever :$u\_\; \backslash rightharpoonup\; u\; \backslash mbox\; X\; \backslash mbox\; j\; \backslash to\; \backslash infty$ (i.e. ''u''''j'' converges weakly to ''u'') and :$\backslash limsup\_\; \backslash langle\; T(u\_),\; u\_\; -\; u\; \backslash rangle\; \backslash leq\; 0,$ it follows that, for all ''v'' ∈ ''X'', :$\backslash liminf\_\; \backslash langle\; T(u\_),\; u\_\; -\; v\; \backslash rangle\; \backslash geq\; \backslash langle\; T(u),\; u\; -\; v\; \backslash rangle.$ 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「Pseudo-monotone operator」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.