query: Which continuous function satisfies $\int\limits_0^x f(t) dt \ge f(x)$ for all $x$ in $[0,1] $?
positive_passages.docid: 154612
positive_passages.text: $\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
negative_passages.docid: 97256
negative_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
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: 147516
negative_passages.text: Continuous function whose right hand derivative equals 0 is constant?
negative_passages.docid: 12349
negative_passages.text: a construction of a continuous function from a normal space to [0,1]
negative_passages.docid: 54137
negative_passages.text: Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable
negative_passages.docid: 120947
negative_passages.text: continuous real-valued function
negative_passages.docid: 52632
negative_passages.text: $f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
negative_passages.docid: 115878
negative_passages.text: Continuous unbounded but integrable functions
negative_passages.docid: 108997
negative_passages.text: Continuous functions that attain local extrema at every point
negative_passages.docid: 103495
negative_passages.text: Let $f$ be continuous. Then $\int_{0}^{x}\left[\int_{0}^{t}f\left(u\right)du\right]dt=\int_{0}^{x}f\left(u\right)\left(x-u\right)du$
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 89421
negative_passages.text: Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?
negative_passages.docid: 55679
negative_passages.text: Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
negative_passages.docid: 29582
negative_passages.text: Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
negative_passages.docid: 132824
negative_passages.text: Does $f$ monotone and $f\in L_{1}([a,\infty))$ imply $\lim_{t\to\infty} t f(t)=0$?
negative_passages.docid: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?