Timeline for For this continuous non differentiable function $f$ How to determine $\sup\{a\}$ s.t $\lim\limits_{h\to0}\frac{f(x+h)-f(x)}{h^\alpha}=0$ for all $x$?

11 events

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Apr 28 at 19:01	comment	added	pie		@SaúlRM If you decided to write write it in detail math.stackexchange.com/questions/4906573/…
Apr 28 at 15:25	comment	added	Saúl RM		I would have to write it in detail, but likely the function $f(x)=\sum_{n\geq1}\frac{1}{n}\cdot\left(\frac{3}{4}\right)^ng(4^nx)$ (where $g$ is as in your question) will work
Apr 28 at 13:43	comment	added	pie		I have other question:Is there a continuous nowhere differentiable function with α− derivative exists at sup{a}? ?
Apr 27 at 14:26	vote	accept	pie
Apr 20 at 6:46	history	edited	Daniele Tampieri	CC BY-SA 4.0	Minor Formatting
Apr 19 at 18:39	comment	added	user479223		It is a very fun exercise and works for any bounded, Lipschitz function.
Apr 19 at 17:41	history	edited	Saúl RM	CC BY-SA 4.0	added 225 characters in body
Apr 19 at 17:37	comment	added	Saúl RM		You are right, it seems this is well known (see here). Well, it was a fun exercise anyways.
Apr 19 at 16:51	comment	added	user479223		By the way, this is just showing that the given function is $-\log_4(3/4)$ Holder. This is the same proof of the Holder continuity of Weierstrass function e.g.
Apr 19 at 2:16	history	edited	Saúl RM	CC BY-SA 4.0	added 431 characters in body
Apr 19 at 1:41	history	answered	Saúl RM	CC BY-SA 4.0