Is the square root a contraction? If yes, there should be only one fixed point; yet, there are two of them, 0 and 1! Thanks for help!
Square root: a contraction?
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real-analysis
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1@Berci: For $x\geq \fr$a$$c${1}{4}$ it is a contraction, too. – 2012-10-23
1 Answers
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You’ve actually answered your own question: it’s not a contraction. I suspect, however, that what you’d really like is an example showing that it’s not a contraction. If $f(x)=\sqrt x$, how does $\left|f\left(\frac14\right)-f(0)\right|$ compare with $\left|\frac14-0\right|\,?$