Generalization of Jakimovski−−Leviatan type Szasz operators

The purpose of this paper is to give a Stancu type generalization of Jakimovski–Leviatan type Szasz operators defined by means of the Sheffer polynomials. We obtain convergence properties of our operators with the help of Korovkin theorem and the order of approximation by using classical and second modulus of continuity. Explicit examples with our operators including Meixner polynomials and the 2-orthogonal polynomials of Laguerre type are given. We present two significant numerical mathematical algorithms as examples for the error estimation.