An easy analytic proof of Brouwer's fixed point theorem (Q2785346)
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scientific article; zbMATH DE number 980853
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An easy analytic proof of Brouwer's fixed point theorem |
scientific article; zbMATH DE number 980853 |
Statements
25 November 1997
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Brouwer's fixed point theorem
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inverse function theorem
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Weierstraß approximation theorem
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transformation formula
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Lebesgue integral
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An easy analytic proof of Brouwer's fixed point theorem (English)
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The author gives a brief elementary proof of Brouwer's fixed point theorem which is based only on the inverse function theorem, the Weierstraß approximation theorem, and the transformation formula for the Lebesgue integral. The author cites a similar proof due to \textit{C. A. Rogers} [Am. Math. Monthly 87, 525-527 (1980; Zbl 0447.57020)], but seems to be unaware of yet another proof of \textit{K. Gröger} [Math. Nachr. 102, 293-295 (1981; Zbl 0484.47032)].
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