Consider the following Volterra integral equation

$$ g(t) = \int_0^t K_n(t,s)w_n(s) ds $$

where g(t) and K_n(t,s) are continuous and $K_n(t,s)\geq K_{n+1}(t,s)$ for all $t,s$. Moreover, $K_n(t,s)$ converges to $K(t,s)$.

The conditions of $K_n(t,s)$ are as follows :

- $K_n(t,s)\neq 0 $ for each n and for all t,s.
- $\frac{\partial K_n(t,s)}{\partial t}$ is continuous.
- $K(t,s)\neq 0 $ for all t,s.

Conditions 1, 2 are sufficient to gurantee the existence of solution $w_n(s)$.

Then, can we say that the solution $w_n(s)$ also converges to some function $w(s)$?

If so, how can i prove it?