Question

Show that if $f $ is $L$-smooth, then $g(x) := f(x) - \frac{m}{2} \Vert x \Vert^2$ is $(L-m)$-smooth

score 701 · Answer 1 · 2026-03-29 18:33:30

701

Views

Show that if $f $ is $L$-smooth, then $g(x) := f(x) - \frac{m}{2} \Vert x \Vert^2$ is $(L-m)$-smooth

Published on 29 Mar 2026 - 18:33

score 93 · Answer 2 · 2021-04-02 13:10:46

93

Views

Picard (Cauchy-Lipschitz) theorem $y'=\sqrt{1+t^2y^2}$, $y(2)=0$

Published on 02 Apr 2021 - 13:10

score 605 · Answer 3 · 2026-03-29 16:49:09

605

Views

Proof involving the sum of $L-$smooth functions

Published on 29 Mar 2026 - 16:49

score 70 · Answer 4 · 2021-04-08 11:24:29

70

Views

Does there exist a Lipschitz injective map whose derivative vanishes on a set of positive measure?

Published on 08 Apr 2021 - 11:24

score 107 · Answer 5 · 2021-04-05 13:20:53

107

Views

How to prove the Lipschitz continuity of the following functions？

Published on 05 Apr 2021 - 13:20

score 657 · Answer 6 · 2021-04-09 15:54:30

657

Views

Does the Sobolev space $W^{1,\infty}(\Omega)$ consist of all bounded Lipschitz functions on $\Omega$ when $\Omega$ is not quasiconvex?

Published on 09 Apr 2021 - 15:54

score 265 · Answer 7 · 2021-04-11 09:05:55

265

Views

Strict convexity and Lipschitz continuity

Published on 11 Apr 2021 - 9:05

score 233 · Answer 8 · 2026-03-30 02:03:35

233

Views

Piecewise approximation for locally Lipschitz function

Published on 30 Mar 2026 - 2:03

score 186 · Answer 9 · 2021-04-13 03:47:55

186

Views

Bound for gradient of a Lipschitz function

Published on 13 Apr 2021 - 3:47

score 79 · Answer 10 · 2021-04-14 21:58:42

79

Views

The closure of the set of all real-valued differentiable functions on $[a,b]$ such that $|f'(x)|\leq K$ for all $x\in [a, b]$. (Kolmogorov and Fomin)

Published on 14 Apr 2021 - 21:58

score 152 · Answer 11 · 2026-03-26 22:17:23

152

Views

Showing a convolution is Lipschitz. In measure.

Published on 26 Mar 2026 - 22:17

score 409 · Answer 12 · 2021-04-22 11:47:38

409

Views

Showing two metric spaces are not bi-Lipschitz equivalent but are uniformly isomorphic

Published on 22 Apr 2021 - 11:47

score 212 · Answer 13 · 2021-04-22 15:09:25

212

Views

"Doubly Lipschitz" functions

Published on 22 Apr 2021 - 15:09

score 356 · Answer 14 · 2021-04-23 01:10:07

356

Views

Any function with a modulus of continuity proportional to any preassigned $\epsilon>0$ is Lipschitz-continuous

Published on 23 Apr 2021 - 1:10

score 54 · Answer 15 · 2021-04-24 07:37:46

54

Views

How to find lipschitz constant of the gradiant of $\sqrt{1+x^2}$?

Published on 24 Apr 2021 - 7:37

List Question

Show that if $f $ is $L$-smooth, then $g(x) := f(x) - \frac{m}{2} \Vert x \Vert^2$ is $(L-m)$-smooth

Picard (Cauchy-Lipschitz) theorem $y'=\sqrt{1+t^2y^2}$, $y(2)=0$

Proof involving the sum of $L-$smooth functions

Does there exist a Lipschitz injective map whose derivative vanishes on a set of positive measure?

How to prove the Lipschitz continuity of the following functions？

Does the Sobolev space $W^{1,\infty}(\Omega)$ consist of all bounded Lipschitz functions on $\Omega$ when $\Omega$ is not quasiconvex?

Strict convexity and Lipschitz continuity

Piecewise approximation for locally Lipschitz function

Bound for gradient of a Lipschitz function

The closure of the set of all real-valued differentiable functions on $[a,b]$ such that $|f'(x)|\leq K$ for all $x\in [a, b]$. (Kolmogorov and Fomin)

Showing a convolution is Lipschitz. In measure.

Showing two metric spaces are not bi-Lipschitz equivalent but are uniformly isomorphic

"Doubly Lipschitz" functions

Any function with a modulus of continuity proportional to any preassigned $\epsilon>0$ is Lipschitz-continuous

How to find lipschitz constant of the gradiant of $\sqrt{1+x^2}$?

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