Suppose $f_{n}$ in $C[0,1]$ all have Lipschitz constant $L$. Show that if $f_{n}$ converges pointwise to $f$, then the convergence is uniform
65474
Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence
13724
What can be said about the convergence on $|z|=1$?
156295
Relax Egoroff's Theorem to pointwise convergence a.e. and bounded a.e. pointwise limit
158344
Uniform continuous maps that converge uniformly to a function f. What can we say about f?
13257
How to prove this problem about uniform continuity
6785
Equicontinuity on a compact metric space turns pointwise to uniform convergence
25532
Determine if the convergence of $f_n(x) = \sqrt{x^2 + \frac{1}{n^2}}$ is uniform.
66758
$f_n:[0,1]\to [0,1]$ continuous, $f_n\to f$ uniformly, prove: ${\frac1n}\sum_{k=1}^{n}{f_k} \to f$ uniformly
156905
Prove $f_n$ has a uniformly convergent subsequence on $[0,1]$.
84818
Convergence of $\sum_{n=1}^{\infty}x_n\overline{y_n}$ for every $(x_n)\in c_0$ implies $\sum_{n=1}^{\infty}|y_n|<\infty$
127251
$f_n(x) = \cos \left( \sqrt{x^2 + \frac{1}{n} }\right)$ is uniformly convergent
155475
$\lim\limits_{n\to \infty} \int_0^1 |f(x)-a_nx-b_n| dx=0$ implies $(a_n)_n,(b_n)_n$ are convergent
142645
$f_n$ converges uniformly on $[a,b]$ to some function $f$
41482
$f_n → f$ 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 $f_n(x_n) → f(x)$.
140972
Uniform convergence of harmonic functions to $0$ on compact subsets
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
93637
Does this sequence converge pointwise and/or in $L^1$?