We give a Kantorovich variant of a generalization of Szasz operators defined by means of the Brenke‐type polynomials and obtain convergence properties of these operators by using Korovkin′s theorem. We also present the order of convergence with the help of a classical approach, the second modulus of continuity, and Peetre′s K‐functional. Furthermore, an example of Kantorovich type of the operators including Gould‐Hopper polynomials is presented and Voronovskaya‐type result is given for these operators including Gould‐Hopper polynomials.

In this paper we introduced the general sequence of linear positive operators via generating functions. Approximation properties of these operators are obtained with the help of the Korovkin Theorem. The order of convergence of these operators computed by means of modulus of continuity Peetre’s K-furictiorial and the elements of the usual Lipschitz class. Also we introduce the r-th order generalization of these operators and we evaluate this generalization by the operators defined in this paper. Finally we give some applications to differential equations.