CONVERGENCE OF URYSOHN-TYPE NONLINEAR INTEGRAL OPERATORS AT p–LEBESGUE POINT

Abstract

In this paper, a general form of the family of Urysohn-type nonlinear integral operators with kernel $K_{\lambda }\left( x,t,g\right) $ is discussed and theorems about the point convergence of this family at ${p}$--Lebesgue points of a function in $L_{p}$ are given. Here, $\lambda$ is the accumulation point and is a positive parameter that changes in the real numbers. Kernel function $K_{\lambda }\left( x,t,g\left( t\right) \right)$ is an entire analytic function with respect to its third variable.