query: If $|f'_n(x)|\leq \frac{1}{\sqrt x}$ and $\int_0^1f_n(x)dx =0$, then exists a subsequence which converges uniformly
positive_passages.docid: 156905
positive_passages.text: Prove $f_n$ has a uniformly convergent subsequence on $[0,1]$.
negative_passages.docid: 30484
negative_passages.text: Radius of convergence and uniformly convergence
negative_passages.docid: 55826
negative_passages.text: Convergence of sequence of real numbers and (sub)subsequence
negative_passages.docid: 129087
negative_passages.text: Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
negative_passages.docid: 56354
negative_passages.text: Uniformly Convergent Subsequence
negative_passages.docid: 106000
negative_passages.text: Determine if $f_n(x)= \big(\cos (\frac x {\sqrt n} )\big )^n $ converges pointwise or/and uniformly?
negative_passages.docid: 111475
negative_passages.text: Uniform convergence and the supremum theorem
negative_passages.docid: 135017
negative_passages.text: Test $f_n = (1+\frac{1}{n^2})^n$ for convergence and give its limit if it exists.
negative_passages.docid: 118362
negative_passages.text: Determine whether $f_n(x)=\frac{x^n}{\sqrt{3n}}$ for $x \in [0,1]$ is uniformly convergent
negative_passages.docid: 97968
negative_passages.text: Does $\big|\sum_{k=1}^na_k\big|\leq\sqrt{n}$ imply the convergence of $\sum_{1}^\infty \frac{a_k}{k}$?
negative_passages.docid: 88147
negative_passages.text: Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
negative_passages.docid: 103124
negative_passages.text: Proving that $f(z)=\sum\limits_{n=1}^{\infty}\frac{z}{n(1+n|z|^{2})}$ converges uniformly on $\mathbb{C}$
negative_passages.docid: 4157
negative_passages.text: Function Sequence Uniform Convergence
negative_passages.docid: 141484
negative_passages.text: Convergence of a sequence by convergence of sub-subsequence
negative_passages.docid: 142645
negative_passages.text: $f_n$ converges uniformly on $[a,b]$ to some function $f$
negative_passages.docid: 152764
negative_passages.text: Let ($x_n$) be a monotone sequence and contain a convergent subsequence. Prove that ($x_n$) is convergent.
negative_passages.docid: 53001
negative_passages.text: If $|f'(c)| \leq M$ and $ M < 1$, the sequence defined by $a_{n+1} = f(a_n)$ converges