On an approximation operator and its Lipschitz constant

Authors

  • Maria Crăciun Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat311-708

Keywords:

approximation operators of Kantorovich type, Sheffer sequences, Lipschitz constants
Abstract views: 189

Abstract

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.

Downloads

Download data is not yet available.

References

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, https://doi.org/10.1016/0021-9045(87)90087-6 DOI: https://doi.org/10.1016/0021-9045(87)90087-6

Craciun, M., Approximation operators constructed by means of Sheffer sequences, Rev. Anal. Numér. Théor. Approx., 30, 2001, pp. 135-150, http://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no2-art3

Lupaş, L. and Lupaş, A., Polynomials of binomial type and approximation operators, Studia Univ. Babeş-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.

Miheşan, 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. Eötvös, 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, https://doi.org/10.1016/0022-247X(73)90172-8 DOI: https://doi.org/10.1016/0022-247X(73)90172-8

Sablonnière, P., Positive Bernstein-Sheffer operators, J. Approx. Theory, 83, pp. 330-341, 1995, https://doi.org/10.1006/jath.1995.1124 DOI: https://doi.org/10.1006/jath.1995.1124

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. Numér. Théor. Approx., 30, pp. 95-105, 2001, http://ictp.acad.ro/jnaat/journal/article/view/2001-vol30-no1-art13

Stancu, D. D. and Occorsio, M. R., On approximation by binomial operators of Tiberiu Popoviciu type, Rev. Anal. Numér. Théor. Approx., 27, pp. 167-181, 1998, http://ictp.acad.ro/jnaat/journal/article/view/1998-vol27-no1-art17

Downloads

Published

2002-02-01

How to Cite

Crăciun, M. (2002). On an approximation operator and its Lipschitz constant. Rev. Anal. Numér. Théor. Approx., 31(1), 55–60. https://doi.org/10.33993/jnaat311-708

Issue

Section

Articles