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Results tagged with real-analysis
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user 31493
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
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Second order difference implies differentiability
Suppose that a function $f$ on the line satisfies $|f(x+2h)-2f(x+h)+f(x)|\le |h|^{3/2}$ for all $x,h$ real. Is it true that $f$ is differentiable and its derivative satisfies
$|f'(x+h)-f'(x)|\le c |h| …
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