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Лемма Скарфа И Теорема Брауэра

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  • Данилов В.И.

Abstract

ЦЭМИ, Москва; E-mail: vdanilov43@mail.ru Аннотация. В статье (Petri, Voorneveld, 2018) было предложено элементарное доказательство теоремы Брауэра о существовании неподвижных точек непрерывного отображения выпуклого компакта в себя. Оно основано на некотором комбинаторном утвержденеии, названном авторами леммой о нетретировании (no-bullying). В настоящей работе мы показываем, что эта лемма является переформулировкой знаменитой леммы Скарфа из классической статьи (Scarf, 1967). Обсуждается также связь нетретирования с понятием уравновешенных состояний, рассмотренных в работе (Данилов, Сотсков, 1987).

Suggested Citation

  • Данилов В.И., 2019. "Лемма Скарфа И Теорема Брауэра," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 55(3), pages 141-143, июль.
    • Handle: RePEc:scn:cememm:v:55:y:2019:i:3:p:141-143
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    1. Petri, Henrik & Voorneveld, Mark, 2018. "No bullying! A playful proof of Brouwer’s fixed-point theorem," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 1-5.
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