Hello.

Let $\displaystyle h: R\longrightarrow{R}$ and consider $\displaystyle f_n(x)= n(h(x + \frac{1}{n})-h(x))$ find necessary and sufficient condition for:

a) $\displaystyle (f_n)$ is punctual convergent.

b) $\displaystyle (f_n)$ is uniform convergent into bounded intervals.

I appreciate every contribution. Thank you so much.