Approximation by modified Favard operators

• Autorzy: Rempulska, L. , Tomczak, K.
• Języki publikacji: EN

Abstrakty

EN

We introduce certain modification of the Favard and Favard-Durrmeyer operators and we give some approximation properties for them. The similar results for the modified Bernstein polynomials are given in [5].

Słowa kluczowe

EN

Favard operator; Favard-Durrmeyer operator; operator; degree of approximation; Voronovskaya theorem

• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr 2
• Strony: 205-215
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Rempulska, L.

• Institute of Mathematics, University of Technology, ul. Piotrowo 3a, 60-965 Poznań, Poland,

autor

Tomczak, K.

• Institute of Mathematics, University of Technology, ul. Piotrowo 3a, 60-965 Poznań, Poland

Bibliografia

• [1] M. Becker, P. L. Butzer and R. J. Nessel, Saturation for Favard operators in weighted function spaces, Studia Math., 19 (1976), 139-153.
• [2] M. Becker, Inverse Theorems for Favard operators in polynomial weight spaces, Commentationes Math., 22 (1981), 165-173.
• [3] P. L. Butzer and R. J. Nessel, Fourier Analysis and Approximation, Vol. I, Academic Press, New York and London, 1971.
• [4] W. Gawroński and U. Stadtmüller, Approximation of continuous functions by generalized Favard operators, J. Approx. Theory, 34 (1982), 384-396.
• [5] G. H. Kirov, A generalization of the Bernstein polynomials, Math. Balkanica, 6 (2), (1992), 147-153.
• [6] G. Nowak and P. Pych-Taberska, Some properties of the generalized Favard-Durrmeyer operators, Functiones et Approx., 29 (2001), 103-112.
• [7] L. Rempulska, M. Skorupka and Z. Walczak, On modified Szász-Mirakyan and Baskakov operators, Grant PB-71-31/03 BW, 2003.