I've read that to insure that a function $g(x)\in C[a,b]$ has a unique fixed point ,is to prove that the absolute values of its derivative $g^{'}(x); x\in]a,b[$ must be less than $1$. what does this concept mean in analysis?
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i think the thing you read is false. e.g. $g \in C[1,2]$, $g(x) = 0$ for $x \in [1,2]$. – mathworker21 Oct 26 '19 at 16:32
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What does "is to prove" mean? Grammatically, this makes no sense. To which concept are you referring? Is it concept of proof, the property of having a derivative bounded by unity, the property of having a unique fixed point or something else? – Carl Christian Oct 27 '19 at 14:57
