On strong approximation of functions of one and two variables by certain operators

• Autorzy: Rempulska L. , Skorupka M.
• Języki publikacji: EN

Abstrakty

EN

We investigate certain class of linear operators in polynomial weighted spaces of differentiable functions of one and two variables. We introduce strong differences of functions and operators and we give approximation theorems for them. The present theorems show that strong approximation is more general than normal approximation. Section I is devoted strong approximation of functions of one variable and Section II of functions of two variables. This note is motivated by resultus on strong approximation connected with Fourier series ([5], [8])

Słowa kluczowe

EN

linear operator; polynomial weighted space; strong approximation

PL

aproksymacja funkcji

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 35
• Strony: 115--133
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Rempulska L.

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

autor

Skorupka M.

• Institute of Mathematice, Poznań University of Technology Piotrowo 3A, 60-965 Poznań, Poland

Bibliografia

• [1] M. Becker, Global approximation theorems for Szász-Mirakyan operators in exponential weight spaces, Indiana Univ. Math. J., (1978), 127-142.
• [2] G.M. Fichtenholz, Calculus, Vol. 1, Warsaw, 1964.
• [3] Z. Finta, Modified Kantorovich polynomials. Math. Balkanica, 13(3-4) (1999), 205-211.
• [4] G.H. Kirov, A generalization of the Bernstein polynomials, Math. Balkanica, 6(2)(1992), 147-153.
• [5] L. Leindler, Strong Approximation by Fourier Series, Akad. Kiado, Budapest 1985.
• [6] L. Rempulska, Z. Walczak, On modified Baskakov operators, Procedings of A. Razmadze Math. Inst, 133(2003), 109-117.
• [7] L. Rempulska, M. Skorupka, On strong approximation of functions by certain operators. Math. J. of Okayama Univ., (in print).
• [8] R. Taberski, Strong summabihty of double Fourier series. Bull. Acad. Polon. Sci., Ser. Sci. Math., 11(1969), 719-726.
• [9] A.F. Timan, Theory of Approximation of Functions of Real Variable, New York, 1963.