Question

Does Continuity Imply Existence (Counter-Example and Confusion)?

score 163 · Answer 1 · 2020-09-25 16:30:14

163

Views

Does Continuity Imply Existence (Counter-Example and Confusion)?

Published on 25 Sep 2020 - 16:30

score 34 · Answer 2 · 2020-09-29 17:28:41

34

Views

$\phi(x) = |x|$ for $x\in [-1,1]$ and $\phi(x+2)=\phi(x)$ for all $x\in \mathbb{R}$. Show $|\phi(t) - \phi(s)|\leq |t-s|$

Published on 29 Sep 2020 - 17:28

score 45 · Answer 3 · 2020-09-30 06:41:31

45

Views

Why do we study Lipschitz continuity condition? (As it is a special case of Holder continuity)

Published on 30 Sep 2020 - 6:41

score 1.1k · Answer 4 · 2026-03-30 05:16:23

1.1k

Views

Applying Picard–Lindelöf theorem for a second order ODE

Published on 30 Mar 2026 - 5:16

score 518 · Answer 5 · 2026-03-30 15:03:45

518

Views

Finding Lipschitz constant from Gradient and Hessian of log-sum-exp

Published on 30 Mar 2026 - 15:03

score 3.4k · Answer 6 · 2020-10-02 10:29:12

3.4k

Views

The exponential function is locally Lipschitz continuous with the Lipschitz constant $K=1$

Published on 02 Oct 2020 - 10:29

score 189 · Answer 7 · 2026-03-25 20:14:16

189

Views

Continuity of solutions to the nonlinear time-varying differential equations in terms of initial states and parameters

Published on 25 Mar 2026 - 20:14

score 726 · Answer 8 · 2026-03-30 16:57:55

726

Views

Upper bound on a function with holder continuous gradient.

Published on 30 Mar 2026 - 16:57

score 526 · Answer 9 · 2020-10-07 10:51:20

526

Views

How to prove that the gradient of nonconvex smooth function is Lipschitz continuous?

Published on 07 Oct 2020 - 10:51

score 366 · Answer 10 · 2020-10-12 12:43:50

366

Views

Let $(X,d)$ be a metric space and fix some $y \in X.$ Show that the function $f: X \to \Bbb R $ defined by $f(x) = d(x,y)$ is Lipschitz continuous.

Published on 12 Oct 2020 - 12:43

score 322 · Answer 11 · 2020-10-14 14:27:45

322

Views

Lipschitz not contraction with a unique fixed point

Published on 14 Oct 2020 - 14:27

score 211 · Answer 12 · 2020-10-18 02:02:52

211

Views

uniformly continuous and Lipschitz

Published on 18 Oct 2020 - 2:02

score 272 · Answer 13 · 2020-10-18 06:43:44

272

Views

Lipschitz constant for two variables function

Published on 18 Oct 2020 - 6:43

score 31 · Answer 14 · 2026-03-30 06:46:57

31

Views

Uniqueness of solution in $x' = 5\text{cos}^2(tx)-x^2-5$

Published on 30 Mar 2026 - 6:46

score 274 · Answer 15 · 2026-03-30 06:30:38

274

Views

Whitney theorem in $C^1$ manifold

Published on 30 Mar 2026 - 6:30

List Question

Does Continuity Imply Existence (Counter-Example and Confusion)?

$\phi(x) = |x|$ for $x\in [-1,1]$ and $\phi(x+2)=\phi(x)$ for all $x\in \mathbb{R}$. Show $|\phi(t) - \phi(s)|\leq |t-s|$

Why do we study Lipschitz continuity condition? (As it is a special case of Holder continuity)

Applying Picard–Lindelöf theorem for a second order ODE

Finding Lipschitz constant from Gradient and Hessian of log-sum-exp

The exponential function is locally Lipschitz continuous with the Lipschitz constant $K=1$

Continuity of solutions to the nonlinear time-varying differential equations in terms of initial states and parameters

Upper bound on a function with holder continuous gradient.

How to prove that the gradient of nonconvex smooth function is Lipschitz continuous?

Let $(X,d)$ be a metric space and fix some $y \in X.$ Show that the function $f: X \to \Bbb R $ defined by $f(x) = d(x,y)$ is Lipschitz continuous.

Lipschitz not contraction with a unique fixed point

uniformly continuous and Lipschitz

Lipschitz constant for two variables function

Uniqueness of solution in $x' = 5\text{cos}^2(tx)-x^2-5$

Whitney theorem in $C^1$ manifold

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