  Approximations of the image and integral funnel of the closed ball of the
space $L_p,$ $p>1,$ under Urysohn type integral operator are considered. The
closed ball of the space $L_p,$ $p>1,$ is replaced by the set consisting of a
finite number of piecewise-constant functions and it is proved that in the
appropriate specifying of the discretization parameters, the images of defined
piecewise-constant functions form an internal approximation of the image of the
closed ball. Applying this result, the integral funnel of the closed ball of
the space $L_p,$ $p>1,$ under Urysohn type integral operator is approximated by
the set consisting of a finite number of points.
