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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 , ∞) 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 , ∞) that do not constitute a subdivision of it. We also discuss the rate of convergence of these operators using moduli of smoothness. [ABSTRACT FROM AUTHOR]

We obtain global rates of approximation by qq-Durrmeyer operators Dn,q(f;x) for the functions in the class Lp([0,1]), 1 ≤ p ≤ ∞. First, rates of approximation in terms of the norms of f and f' and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness ωφ(f,δ). [ABSTRACT FROM AUTHOR]