Abstract
The purpose of the present paper is to introduce and study a sequence of positive linear operators defined on suitable spaces of measurable functions on [0, infinity) and continuous function spaces with polynomial weights. These operators are Kantorovich type generalization of Jakimovski-Leviatan operators based on multiple Appell polynomials. Using these operators, we approximate suitable measurable functions by knowing their mean values on a sequence of subintervals of [0, infinity) that do not constitute a subdivision of it. We also discuss the rate of convergence of these operators using moduli of smoothness.