Hi could you help me with the following:
If I have a function $g \in C^2(0,R)$ with $|g''(x)| \le M$, i.e. its second derivative is bounded except a finite number of points where at those irregularity points none of the assumptions mentioned above holds can you give me a sequence of functions $f_n$ with $f_n^\prime \longrightarrow g'$ and $f_n \longrightarrow g$ uniformly and $|f_n^{\prime\prime}(x)| \le M$?
I think about polynomials but can not justify that they have all the requirements??
Thanks a lot!!