A new class of Bernstein-type operators obtained by iteration
DOI:
https://doi.org/10.24193/subbmath.2023.2.15Keywords:
modified Bernstein operators, degree of approximations, Voronovskaja theorem, higher order convexity, simultaneous approximationAbstract
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.References
bibitem{CTLX} Chen, X., Tan, J., Liu, Z., Xie J., emph{Approximation of functions by a new family
of generalized Bernstein operators}, J. Math. Anal. Appl., {bf 450}(2017), 244--261.
bibitem{Go07} Gonska, H., emph{On the degree of approximation in Voronovskaja’s theorem}, Stud. Univ. Babec s-Bolyai. Math., {bf 52}(2007), no. 3, 103-115.
bibitem{KP} Knopp, H.P., Pottinger, P., emph{Ein Satz vom Korovkin-Typ f"ur $C^k$-R"aume}, Math. Z., {bf 148}(1976) 23-32.
bibitem{Mo} Mond, B., emph{Note: On the degree of approximation by linear positive operators},
J. Approx. Theory, {bf 18}(1976), 304-306.
bibitem{RP04} Pu altu anea, R., emph{Approximation theory using positive linear operators}, Birkh"auser, Boston, 2004.
bibitem{Po} Popoviciu, T., emph{Les fonctions convexes} (French), Actualit'es Sci. Ind., {bf 992}, Hermann et Cie, Paris, 1944.
bibitem{SM} Smuc, M., emph{On a Chlodovsky variant of $alpha$-Bernstein operator}, Bull. Transilv. Univ. Brac sov Ser. III. Math. Inform. Phys., {bf 10(59)}(2017), no. 1, 165-178.
Downloads
Additional Files
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
