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The Voronovskaya type theorem for Poisson integrals of functions of two variables

Krech G.

Commentationes Mathematicae

2013

Vol 53, No. 1

23--34

The aim of this paper is the study the Voronovskaya type theorem for Poisson integrals of functions of two variables for Hermite and Laguerre expansions. We also present some boundary value problems related to these integrals.

Approximation by bivariate Mazhar-Totik operators

Wachnicki E.

Commentationes Mathematicae

2010

Vol. 50, [Z] 2

141-153

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.

Certain modification of Szasz-Mirakyan operators

Walczak Z.

Fasciculi Mathematici

2004

Nr 34

141-147

We consider certain modified Szasz-Mirakyan operators An (f; r) in space C0 of uniformly continuous functions. We study approximation properties of these operators.

Approximation by modified Favard operators

Rempulska L., Tomczak K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 2

205-215

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].

Approximation of functions of one and two variables by some operators

Rempulska L., Skorupka M.

Fasciculi Mathematici

2002

Nr 33

57-87

We consider some operates of Szasz-Mirakyan type in exponential weighted spaces of functions of one and two variables. We give theorems on the degree of approximation of functions by these operators and the Voronovskaya type theorems.

The Voronovskaya type theorem for the Baskakov-Kantorovich operators

Bogalska K.

Fasciculi Mathematici

1999

Nr 30

5-13

In this paper we give the Voronovskaya type theorem for the Baskakov-Kantorovich operators in the polynomial weighted spaces. The Baskakov operators were studied in [l]. The Voronovskaya type theorem for some operators are given in [2], [3].