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Let $f(x)$ be a monotone non-decreasing convex function such that its derivative $\frac{d}{dx}f(x) = f'(x)$ is also a convex function. Is there a term in literature that is used to refer to such functions? I would appreciate a reference if possible.

Just to be clear, this does not coincide with the definition of strict convexity or strong convexity. For example: $f(x) = 0$ is a convex function whose derivative is also trivially convex but this is not strictly convex. The definition above captures functions whose third derivative is also non-negative.

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  • $\begingroup$ I do not believe there is a special term for such functions. $\endgroup$ – Michael Grant Feb 17 '15 at 1:45

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