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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 Earle–Hamilton fixed-point theorem ： ウィキペディア英語版 Earle–Hamilton fixed-point theorem In mathematics, the Earle–Hamilton fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping of an open domain in a complex Banach space into itself to have a fixed point. The result was proved in 1968 by Clifford Earle and Richard Hamilton by showing that, with respect to the Carathéodory metric on the domain, the holomorphic mapping becomes a contraction mapping to which the Banach fixed-point theorem can be applied. ==Statement== Let ''D'' be a connected open subset of a complex Banach space ''X'' and let ''f'' be a holomorphic mapping of ''D'' into itself such that: *the image ''f''(''D'') is bounded in norm; *the distance between points ''f''(''D'') and points in the exterior of ''D'' is bounded below by a positive constant. Then the mapping ''f'' has a unique fixed point ''x'' in ''D'' and if ''y'' is any point in ''D'', the iterates ''f''''n''(''y'') converge to ''x''. 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「Earle–Hamilton 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.