I've been stuck on this problem for a bit now:
Let $g$ and $f_0$ be continuous functions on $[0,1]$. Define the sequence on $[0,1]$ by $$f_n(x) = \int_0^t g(t)f_{n-1}dt.$$
I have to prove that the sequence is converges uniformly.
Here are my thoughts: I know $f_n$'s are continuous and I also tried to solve this question using the $\epsilon-\delta$ definition for continuity and uniform convergence without any luck.
Any hint?