Sheffer polynomials and approximation operators

Abstract

In this paper we are studying the sequence of linear positive operators $(P_n^{(Q,S)})$ defined in (2). Using the Bohman-Korovkin uniform convergence criterion we are proving that the sequence $(P_n^{(Q,S)})$ converges uniformly to the identity operator.
 noindent In addition we give some estimates. Finally we consider two examples $(P_n^{(A,S)})$ and $(P_n^{(na,S)})$ defined in (25), (27).

General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints

“…Appell polynomials have many applications in various disciplines: probability theory [1][2][3][4][5], number theory [6], linear recurrence [7], general linear interpolation [8][9][10][11][12], operators approximation theory [13][14][15][16][17]. In [18], P. Appell introduced a class of polynomials by the following equivalent conditions: {A n } n∈IN is an Appell sequence (A n being a polynomial of degree n) if either…”