On the rate of approximation of absolutely continuous functions by certain Kantorovich-type operators

• Autorzy: Pych-Taberska, P.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to present estimates for the rate of pointwise convergence of the kantorovichians of the discrete Feller operators in some classes of absolutely continuous functions, in particular, for functions with derivatives of bounded variation in the generalized sense.

Słowa kluczowe

EN

Kantorovich type operator; rate of convergence; asymptotic formula

• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 193-202
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Pych-Taberska, P.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland,

Bibliografia

• [1] G. D. Bai, Y. H. Hua and S. Y. Shaw, Rate of approximation for functions with derivatives of bounded variation, Analysis Math. 28 (2002), 171-196.
• [2] R. Bojanic and F. Cheng, Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation, J. Math. Anal. Appl. 141 (1989), 136-151.
• [3] R. Bojanic and M. K. Khan, Rate of convergence of some operators of functions with derivatives of bounded variation, Atti Sem. Mat. Fis. Univ. Modena 39 (1991), 495-512.
• [4] W. Feller, An Introduction to Probability Theory and its Applications, Vol. II, Wiley, New York, 1966.
• [5] M. Heilmann, Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory and its Appl. 5 (1989), 105-127.
• [6] P. Pych-Taberska, Rate of pointwise convergence of Bernstein polynomials for some absolutely continuous functions, J. Math. Anal. Appl, 212 (1997), 9-19.
• [7] P. Pych-Taberska, Pointwise approximation of absolutely continuous functions by certain linear operators, Functiones et Approximatio 25 (1997), 67-76.

Uwagi

To Professor Julian Musielak on his 75th birthday.