query: Uniformly continuous functions sequence $f_n(x)$ converges uniformly to a uniformly continuous function $f(x)$?
positive_passages.docid: 158344
positive_passages.text: Uniform continuous maps that converge uniformly to a function f. What can we say about f?
negative_passages.docid: 115840
negative_passages.text: Showing equality of sequence of holomorphic functions to limit function if converges uniformly locally
negative_passages.docid: 66758
negative_passages.text: $f_n:[0,1]\to [0,1]$ continuous, $f_n\to f$ uniformly, prove: ${\frac1n}\sum_{k=1}^{n}{f_k} \to f$ uniformly
negative_passages.docid: 101906
negative_passages.text: Why is this sequence of equicontinuous functions uniformly bounded?
negative_passages.docid: 51247
negative_passages.text: $f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
negative_passages.docid: 813
negative_passages.text: $f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
negative_passages.docid: 41482
negative_passages.text: $f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
negative_passages.docid: 65312
negative_passages.text: Check the uniform convergence of series of functions
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
negative_passages.docid: 111475
negative_passages.text: Uniform convergence and the supremum theorem
negative_passages.docid: 117649
negative_passages.text: $f:[0,1]\to[0,1]$ be a continuous function. Let $x_1\in[0,1]$ and define $x_{n+1}={\sum_{i=1}^n f(x_i)\over n}$.Prove, $\{x_n\}$ is convergent
negative_passages.docid: 35547
negative_passages.text: Does $\{f_ng_n\}\to fg$ uniformly?
negative_passages.docid: 10408
negative_passages.text: Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
negative_passages.docid: 155822
negative_passages.text: Does uniform convergence preserves absolute continuity?
negative_passages.docid: 12997
negative_passages.text: Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?
negative_passages.docid: 98762
negative_passages.text: $f_n(x) = x - x^n$ for $x\in [0,1]$. Does the sequence converge pointwise or uniformly on $[0,1]$?
negative_passages.docid: 127224
negative_passages.text: Sequence uniform convergence but the derivatives are not.