  We investigate the problem of pointwise convergence of the family of
non-linear integral operators: \begin{equation} L_\lambda(f,x) = \int_a^b
\sum_{m=1}^N f^m(t) K_{\lambda ,m}(x,t) dt, \end{equation} where $\lambda $ is
a real parameters, $K_{\lambda ,m}(x,t)$ is non-negative kernel and $f$ is the
function in $L_{1}(a,b)$. We consider two cases where $% (a,b)$ is a finite
interval and when is the whole real axis.
