A new class of Bernstein-type operators obtained by iteration

Radu Paltanea, Mihaela Smuc

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.

Keywords


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

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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.




DOI: http://dx.doi.org/10.24193/subbmath.2023.2.15

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