Some results on generalized Szász operators involving Sheffer polynomials

Abstract

In this paper we consider old and new operators of Szász type involving Sheffer polynomials. We present an asymptotic expansion formula for operators of Ismail type. Then, in order to improve the accuracy of the approximation of a function $f$ in a fixed point, we apply a well-known extrapolation algorithm. We also introduce some new special sequences of Appell and Sheffer polynomials and construct new generalized Szász-type operators. By using classical techniques we investigate approximation properties and rate of convergence for these operators and compare the results with other existing operators. Finally, we present numerical examples which confirm the validity of the theoretical analysis and the effectiveness of the presented operators.