Hölder Continuity

Hölder Continuity Definition and Properties
In this video, I define the notion of Hölder continuity and show that any Hölder continuous function must be uniformly continuous. I then give some interesting properties of Hölder continuity
Uniform Continuity: • What is Uniform Contin...
Weak Derivative: • The Weak Derivative
Continuity Playlist: • Limits and Continuity
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[@mudkip_btw]

I feel like I slowly learn a lot from your videos just by watching once or twice per week. Things I kind of know about, but since I study physics, don't pay all to much attention to. Thanks a bunch dr. πm!

[@drpeyam]

Thanks so much!!!

[@themattsone5192]

Nice Richter Alexander Hold reference 😂😂

[@him21016]

Very nice to see more frequent uploads. Real analysis is a hard subject to learn from Wikipedia articles only

[@juanblanc_079]

I'm starting in this incredible path of mathematics. Nice to see people teaching with passion and comprehensibility such a complex topic (at least for myself). Greetings from Colombia

[@ComplexVariables]

Love a video that starts with a clear, written definition.

[@Thisalwerasekara]

The best short and descriptive explanation I've ever seen about Hölder Continuity! Thank you!

[@vijayamanikandan2045]

Best explanation. Thanks.

[@ThinkDifferentlier]

Thank you, I was waiting for a vid about Hölder&Lipschitz continuity.

[@nataliawrozek3867]

You really helped me millions, I love your energy! I struggled a bit with these continuety stuff and I don't anymore, thanks a lot!

[@drpeyam]

Glad I could help :)

[@theinvisiblearmadilloofdea6204]

Thanks, this was very helpful!

[@insouciantFox]

Wonderful! Just what I wanted, thanks!

[@srikanthtupurani6316]

There are so many strange banach spaces with very complex norms which are very useful in pdes. Can you make some video on sobolev spaces.

[@hiteshsblog5409]

Very helpful.... 💐☺

[@malouselle8031]

Merci pour tes vidéos

[@drpeyam]

De rien ☺️

[@yajunhua2420]

Very helpful! Thanks!

[@darkpikachu_.]

i like how you say hölder

[@uhbayhue]

This was really cool, thanks!

[@Monirul2512]

Very nice❤❤❤❤ do more videos sir

[@neilgerace355]

FYI Richter means judge. In my German class in high school we studied a novel called "Der Richter und sein Henker" = The Judge and his Hangman.

[@dgrandlapinblanc]

Ok. Thanks.

[@cristhianleninmasaquizaver383]

Buen video. Saludos desde Ecuador 🇪🇨

[@personxy7443]

sir,Is there about Fourier series convergence?dini condition,dirichlet condition,remann lebesgue lemma,holder continuos condtion,these mess up

[@dogatokgoz5594]

abi çok sağol çok yardımcı oldu

[@pythoncake2708]

will there by a continuation (pun intended) including a Barbara Salesch reference? :D

[@drpeyam]

That would be awesome 😂 One where I wear a red wig haha

[@nawzadhogan5130]

Quick question, if you take (X,d) and (Y,d') to be two metrics, and f : X -> Y a-Holder function with a>1, is f still constant ? The proof given in the case where X = Y = R doesn't apply

[@drpeyam]

I don’t think so, I’m sure there are counterexamples with the discrete metric

[@yoav613]

This is the easiest scratch work ever!

[@aneeshsrinivas9088]

Why is the wierstrass function holder continuous as you say?

[@aneeshsrinivas9088]

Is the proof far beyond the scope of the class you’re teaching?

[@mathemitnawid]

I like the title of the Video 😅🙌🙌

[@Happy_Abe]

When alpha is greater than 1, how do we know f(x) is differentiable to make that argument from the derivative being 0?

[@SlipperyTeeth]

He actually just showed that it is by computing the value. By 8:32 all he's done is just algebra. Then he takes the limit as h approaches 0, the left side is the definition of the absolute value of the derivative of f which at this point may not exist, the right side is obviously 0, then by the squeeze theorem, the left side must exist and must be 0.
If the right side wasn't 0, we couldn't say much about the limit of the left side, but we could still put bounds on the limsup and liminf. If it makes you feel more comfortable, you could take the limsup and liminf since they always exist as opposed to the lim which may not. Then see that they are both equal (specifically to 0) and thus you'd be justified in taking the lim which is the definition of the derivative. In practice though, the squeeze theorem is well known and if you know the derivative will exist it's fair to just compute it.

[@drpeyam]

Phoenix Fire Great explanation

[@Happy_Abe]

Thank you for explaining and confirming!

[@SlipperyTeeth]

@@drpeyam Thank you. You as well - great video

[@SlipperyTeeth]

@@Happy_Abe No problem, it's a pleasure

[@AnishThe01]

Sir Can you suggest me some resource so that I can master the calculas and up to a great level.
-😊😊

[@drpeyam]

My playlists

[@BlokenArrow]

@@drpeyambprp

[@ilickcatnip]

@@drpeyam Yes they're awesome!

[@MevTrades]

I think he gonna cry at any time.🤣🤣

[@nachiketakumar9645]

Are you Indian?

[@drpeyam]

Nope