We prove theorems on convergence of multidimensional nonlinear integrals in Lebesgue points of generated function, and show that the main results are applicable to a wide class of exponentially nonlinear integral operators, which may be constructed by using well known positive kernels in approximation theory.
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 L1−function. The kernel Kλ(x,t,u(t)) depends on the positive parameter λ changing on the set of numbers with the accumulation point at infinity and Kλ(x,t,u(t)) is an entire analytic function of variable u, which is a bounded function belonging to L1(R).
We prove a theorem on weighted pointwise convergence of \ multidimensional integral operators with radial kernels to generating function of several variables, which are in general non-integrable in $n$-dimensional Euclidean space $E_{n}$ in the sense of Lebesgue$.$ Main result holds at almost every point of $E_{n}.$
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