query: Integral map $Tf(x)=\int_{0}^{x} f(s) d s$ is not a contraction on $C[0,1]$?
positive_passages.docid: 27775
positive_passages.text: Proving a function is not a contraction
negative_passages.docid: 35569
negative_passages.text: Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
negative_passages.docid: 37015
negative_passages.text: Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
negative_passages.docid: 110395
negative_passages.text: Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
negative_passages.docid: 135577
negative_passages.text: Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
negative_passages.docid: 15175
negative_passages.text: When does a Möbius transformation map $\Im(z)>0$ to itself?
negative_passages.docid: 19072
negative_passages.text: $\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
negative_passages.docid: 93681
negative_passages.text: Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
negative_passages.docid: 47211
negative_passages.text: Does $\varphi(x)\le\int_0^x\varphi(t)dt$ for all $x\in[0,\infty)$ imply $\varphi\equiv0$.
negative_passages.docid: 66409
negative_passages.text: Show that the linear operator $(Tf)(x)=\frac{1}{\pi} \int_0^{\infty} \frac{f(y)}{(x+y)} dy$ satisfies $\|T\|\leq 1$.
negative_passages.docid: 19245
negative_passages.text: Schwartz Distribution Theory: (Non-)Surjectivity of $f \mapsto f*f$ in $ \mathcal E '$
negative_passages.docid: 18825
negative_passages.text: Integrable but not differentiable function
negative_passages.docid: 33485
negative_passages.text: norm of integral operator in $C([0,1])$
negative_passages.docid: 72115
negative_passages.text: Why isn't there a continuously differentiable surjection from $I \to I \times I$?
negative_passages.docid: 102914
negative_passages.text: Integral domain that is not a factorization domain
negative_passages.docid: 71071
negative_passages.text: Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
negative_passages.docid: 101778
negative_passages.text: Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$