On the strong approximation of functions by the Bernstein polynomials

• Autorzy: Michałowicz A.
• Języki publikacji: EN

Abstrakty

EN

In this note we introduce the strong differences of function and its Bernstein polynomials and give approximation theorems for them. This note is motivated by results on the strong summability of trigonometric Fourier series given in [2] and by the paper [5].

Słowa kluczowe

EN

Bernstein polynomial; strong difference; degree of approximation

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2007
• Tom: Nr 37
• Strony: 27--33
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Michałowicz A.

Bibliografia

• [1] DE VORE R.A., The Approximation of Continuous Functions by Positive Linear, Operators, New York, 1972.
• [2] LEINDLER L., Strong Approximation by Fourier Series, Akad.Kiado, Budapest 1985..
• [3] ŁOJASIEWICZ S., Introduction to Theory of a Real Functions, Warsaw 1976, (in Polish).
• [4] NATANSON I.P., Constructive Theory of Functions, Moskow 1949, (in Russian).
• [5] REMPULSKA L., SKORUPKA M., On Strong Approximation of Functions by Certain, Linear Operators, Math. J. of Okayama Univ., 46(2004), 153-161.
• [6] TIMANN A.F., Theory of Approximation of Functions of a Real Variable, New York, 1963.