On pointwise convergence of the family of Urysohn-type integral operators

Abstract

In this paper, we consider a family of nonlinear integral operators of Urysohn-type and study the pointwise convergence of the family at characteristic points of L-1-function. The kernel K-lambda(x, t, u(t)) depends on the positive parameter lambda changing on the set of numbers with the accumulation point at infinity and K-lambda(x, t, u(t)) is an entire analytic function of variable u, which is a bounded function belonging to L-1(R).