New posts in uniform-convergence

Number of roots of a sequence of a uniformly convergent holomorphic functions implies an upper bound for the number of roots of their limit

complex-analysis analysis convergence-divergence uniform-convergence

Uniform convergence of real part of holomorphic functions on compact sets

complex-analysis uniform-convergence

Definitions of Lebesgue integral

integration measure-theory lebesgue-integral uniform-convergence

If $\sum A_n$ converges, does $\sum A_n x^n$ converge uniformly on $[0,1]$?

real-analysis sequences-and-series uniform-convergence

Uniform Convergence verification for Sequence of functions - NBHM

real-analysis proof-verification uniform-convergence alternative-proof

Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism

general-topology analysis uniform-convergence

Complex Analysis -- Uniform Convergence on Compact Sets

complex-analysis uniform-convergence

Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?

analysis functional-analysis uniform-convergence

why is $\sum_{n=1}^{\infty} \frac{1}{n} \sin\left( \frac{x^n}{\sqrt n} \right)$ uniformly convergent? [duplicate]

sequences-and-series uniform-convergence

Is this sequence Cauchy?

real-analysis uniform-convergence cauchy-sequences

Prove that a linear subspace of $C([0,1])$ is closed

functional-analysis vector-spaces uniform-convergence

Uniform convergence when $a \lt b$ but not if $a \geq b$

real-analysis convergence-divergence uniform-convergence supremum-and-infimum pointwise-convergence

Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.

real-analysis limits proof-verification uniform-convergence sequence-of-function

$f_n(x_n) \rightarrow f(x) $ by uniform convergence

real-analysis uniform-convergence

Is this sequence of functions uniformly convergent on $[0,1]$?

limits uniform-convergence

Prove $ \lim_{h\rightarrow 0}\frac{1}{h}\int_a^x[f(t+h)-f(t)]\mathrm{d}t=f(x)-f(a). $

calculus integration analysis multivariable-calculus uniform-convergence

Unit ball in $C[0,1]$ not sequentially compact

sequences-and-series functional-analysis convergence-divergence compactness uniform-convergence

Suppose $ \sum a_k x^k $ uniformly converges at $ [0,R) $, then it converges pointwise at $ R $.

convergence-divergence power-series uniform-convergence

Can a sequence of unbounded functions be uniformly convergent?

real-analysis uniform-convergence

How to prove that $\,\,f\equiv 0,$ without using Weierstrass theorem?

real-analysis integration analysis polynomials uniform-convergence