$f(x)$ is a bounded continuous real function on $\mathbb{R}$.And $f(x)$ satisfies that
$$\lim_{h\to0}\sup_{x\in\mathbb{R}}|f(x+h)-2f(x)+f(x-h)|=0$$
Prove that $f(x)$ is uniformly continuous on $\mathbb{R}$.
I have thought of this question for a long time,but I cannot solve it.Any hint will be helpful.Thanks!
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Walt.White
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2Why do you want me to do that? – José Carlos Santos Apr 02 '21 at 15:00
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See https://math.stackexchange.com/q/3978738/42969 – Martin R Apr 02 '21 at 15:06
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@JoséCarlosSantos I have thought it for a long time,but I hardly have any idea.I need some hints. – Walt.White Apr 02 '21 at 15:07
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@MartinR Thanks!It's really helpful. – Walt.White Apr 02 '21 at 15:09