An effective construction of a discrete analogue of functions with a bounded second derivative (Q1280343)

The condition \[ \big| g(x)-2g(x+h)+g(x+2h)\big| \leq \dfrac{Ch^2}{N} + 2,\tag{1} \] where \(g\) is the discrete function: \(g\:\{0,1,\dots,N-1\}\to \{0,1,\dots,N-1\}\) is called by the author the discrete analogue of the condition \(| f''(x)| \leq C\). For the class of functions \(g\) satisfying the condition (1) found are the growth order of the power logarithm of minimal 1-approximating set and the complexity order of 1-approximated calculation by schemes of functional elements.