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

Approximations of the Image and Integral Funnel of the $L_p$ Ball under Urysohn Type Integral Operator