A new class of Bernstein-type operators obtained by iteration

Authors

  • Radu PĂLTĂNEA “Transilvania” University, Faculty of Mathematics and Computer Sciences, 50, Maniu Iuliu Street, 500091 Bra¸sov, Romania e-mail: radupaltanea@yahoo.com https://orcid.org/0000-0002-9923-4290
  • Mihaela SMUC “Transilvania” University, Faculty of Mathematics and Computer Sciences, 50, Maniu Iuliu Street, 500091 Bra¸sov, Romania e-mail: mihaela_smuc@yahoo.com

DOI:

https://doi.org/10.24193/subbmath.2023.2.15

Keywords:

Modified Bernstein operators, degree of approximations, Voronovskaja theorem, higher order convexity, simultaneous approximation.

Abstract

A new class of Bernstein-type operators are obtained by applying an iterative method of modifications starting from the Bernstein operators. These operators have good properties of approximation of functions and of their derivatives.

Mathematics Subject Classification (2010): 41A36, 41A10, 41A25.

Received 23 February 2022; Accepted 22 September 2022.

References

Chen, X., Tan, J., Liu, Z., Xie, J., Approximation of functions by a new family of generalized Bernstein operators, J. Math. Anal. Appl., 450(2017), 244-261.

Gonska, H., On the degree of approximation in Voronovskaja’s theorem, Stud. Univ. Babeș-Bolyai. Math., 52(2007), no. 3, 103-115.

Knopp, H.P., Pottinger, P., Ein Satz vom Korovkin-Typ für Cᵏ -Räume, Math. Z., 148(1976), 23-32.

Mond, B., Note: On the degree of approximation by linear positive operators, J. Approx. Theory, 18(1976), 304-306.

Păltănea, R., Approximation Theory Using Positive Linear operators, Birkhäuser, Boston, 2004.

Popoviciu, T., Les Fonctions Convexes (French), Actualités Sci. Ind., 992, Hermann et Cie, Paris, 1944.

Smuc, M., On a Chlodovsky variant of α-Bernstein operator, Bull. Transilv. Univ. Brașov Ser. III. Math. Inform. Phys., 10(59)(2017), no. 1, 165-178.

Downloads

Published

2023-06-14

How to Cite

PĂLTĂNEA, R., & SMUC, M. (2023). A new class of Bernstein-type operators obtained by iteration. Studia Universitatis Babeș-Bolyai Mathematica, 68(2), 409–422. https://doi.org/10.24193/subbmath.2023.2.15

Issue

Section

Articles

Similar Articles

<< < 2 3 4 5 6 7 8 9 10 11 > >> 

You may also start an advanced similarity search for this article.