Approximation by bivariate Mazhar-Totik operators

• Autorzy: Wachnicki E.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to study a bivariate version of the operator investigated in [2], [4]. We shall present Voronovskaya type theorem and theorems giving a rate of convergence of this operator. Some applications for the limit problem are indicated.

Słowa kluczowe

EN

positive linear operator; rate of convergence; Voronovskaya theorem; modulus of continuity; modulus of smoothness; mixed modulus of smoothness; limit problem

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: Vol. 50, [Z] 2
• Strony: 141--153
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Wachnicki E.

• Institute of Mathematics, Pedagogical University ul. Podchorążych 2, 30-084 Kraków, Poland,

Bibliografia

• [1] W. Magnus and F. Oberhettinger, Formelen und S¨atz f¨ur die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin 1948.
• [2] S. M. Mazhar and V. Totik, Approximation by modified Szász operators, Acta Sci. Math. (Szeged) 49 (1985), 257-269.
• [3] A. F. Timan, Theory of Approximation of Functions of a Real Variable, Moscow 1960 [in Russian].
• [4] E. Wachnicki, On generalized Mazhar-Totik operators, Demonstratio Math. 38.1 (2005), 143-151.