In this note we consider an approximation operator of Kantorovich type in which expression appears a basic sequence for a delta operator and a Sheffer sequence for the same delta operator.
We give a convergence theorem for this operator and we find its Lipschitz constant.
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
approximation operators of Kantorovich type; Sheffer sequences; Lipschitz constants.
M. Crăciun, On an approximating operator and its Lipschitz constant, Rev. Anal. Numér. Théor. Approx., vol. 31 (2002), no. 1, 55-60.
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 Agratini, O., On a certain class of approximation operators, Pure Math. Appl., 11, pp. 119–127, 2000.
 Brown, B. M., Elliot, D. and Paget, D. F., Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory, 49, pp. 196–199, 1987.
 Craciun, M., Approximation operators constructed by means of Sheffer sequences, Rev. Anal. Numer. Theor. Approx., 30, 2001, pp. 135–150.
 Lupas, L. and Lupas, A., Polynomials of binomial type and approximation operators, Studia Univ. Babe¸s-Bolyai, Mathematica, 32, pp. 61–69, 1987.
 Manole, C., Approximation operators of binomial type, Univ. Cluj-Napoca, Research Seminar on Numerical and Statistical Calculus, Preprint no. 9, pp. 93–98, 1987.
 Mihesan, V., Approximation of continuous functions by means of linear positive operators, Ph.D. Thesis, Cluj-Napoca, 1997 (in Romanian).
 Moldovan, G., Discrete convolutions and linear positive operators, Ann. Univ. Sci. Budapest R. E¨otv¨os, 15, pp. 31–44, 1972.
 Popoviciu, T., Remarques sur les polynomes binomiaux, Bull. Soc. Math. Cluj, 6, pp. 146–148, 1931.
 Rota, G.-C., Kahaner, D. and Odlyzko, A., On the foundations of combinatorial theory. VIII. Finite operator calculus, J. Math. Anal. Appl., 42, pp. 684–760, 1973.
 Sablonniere, P., Positive Bernstein-Sheffer operators, J. Approx. Theory, 83, pp. 330–341, 1995.
 Stancu, D. D., Approximation of functions by a new class of linear positive operators, Rev. Roum. Math. Pures Appl., 13, pp. 1173–1194, 1968.
 Stancu, D. D., On the approximation of functions by means of the operators of binomial type of Tiberiu Popoviciu, Rev. Anal. Numer. Theor. Approx., 30, pp. 95–105, 2001.
 Stancu, D. D. and Occorsio, M. R., On approximation by binomial operators of Tiberiu Popoviciu type, Rev. Anal. Numer. Theor. Approx., 27, pp. 167–181, 1998.