Teorema di Altman

Questa voce sull'argomento geometria è solo un abbozzo.

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In matematica, il teorema di Altman è un teorema di punto fisso che generalizza il teorema di Rothe, a sua volta un'estensione del risultato di Schauder.

Enunciato

Sia $A$ un insieme limitato, aperto, convesso in uno spazio di Banach $X$ , con $0\in A$ . Detto ${\overline {A}}$ la chiusura di $A$ , sia inoltre $f\colon {\overline {A}}\to X$ una funzione completamente continua tale che:

\|x-f(x)\|^{2}\geq \|f(x)\|^{2}-\|x\|^{2}\qquad x\in \partial A

con $\partial A$ la frontiera di $A$ . Allora $f$ ha un punto fisso.

Voci correlate

Collegamenti esterni

(EN) Sadayuki Yamamuro - Some fixed point theorems in locally convex linear spaces (PDF), su kamome.lib.ynu.ac.jp. URL consultato il 4 giugno 2015 (archiviato dall'url originale il 5 giugno 2015).

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