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Proposition: Fixed-Point Property of Continuous Functions on Closed Intervals

Let $[a,b]$ be a closed real interval and let $f:[a,b]\to[a,b]$ be a continuous function. Then $f$ has a fixed point property, i.e. there is an $x\in[a,b]$ with $f(x)=x.$

Table of Contents

Proofs: 1

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983