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Convergence of the sequence of maxima of a function sequence

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#sequences-and-series #convergence-divergence #uniform-convergence
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Convergence of the sequence $f_n(x)=\frac{1}{1+nx^2}$

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#sequences-and-series #convergence-divergence #uniform-convergence
103
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Uniform convergence of $\sum f(x)^n$

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#sequences-and-series #convergence-divergence #uniform-convergence
236
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uniform convergence in sequence particularly infinite matrix

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#uniform-convergence
98
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Pointwise/Uniform Convergence of a function

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#convergence-divergence #uniform-convergence
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Let $f_n(x)=nx(1-x^2)^n$ on $[0,1]$ for $n\ge1$. Find $f(x)= \lim f_n(x)$. Is this a convergence uniform?

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#real-analysis #uniform-convergence
240
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Disprove uniform convergence of $x^n$ where $ x\in[0,1)$

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#uniform-convergence
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Let $f_n(x)=xne^{-nx}$ for all $x \ge 0$ and $n \ge 1$. Show that $(f_n)$ converges to zero on $[0, \infty)$ pointwise but not uniformly

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#real-analysis #uniform-convergence
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Does the sequence$ f_n(x)=\frac{x}{1+nx^2}$ converge uniformly on $\mathbb{R}$?

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#real-analysis #uniform-convergence
121
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Mollifiers: Uniform Convergence

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#real-analysis #functional-analysis #uniform-convergence
211
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$k_n(x) = \frac x{1+nx^2}$ uniform convergence

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#real-analysis #sequences-and-series #analysis #uniform-convergence
636
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Proving uniform convergence of an integral-defined function on compact sets

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#compactness #lebesgue-integral #uniform-convergence
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Uniform convergence of a sequence of functions and equicontinuity

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#real-analysis #metric-spaces #uniform-convergence #equicontinuity
55
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Prove $\{h_n\}_{n=1}^\infty$ converges uniformly on $[a,1]$

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#real-analysis #sequences-and-series #analysis #uniform-convergence
1.1k
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Prove that function is not uniformly convergent

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#calculus #uniform-convergence

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