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Direct estimate for some operators of Durrmeyer type in exponential weighted space

Krech G., Wachnicki E.

Demonstratio Mathematica

2014

Vol. 47, nr 2

336--349

In the present paper, we investigate the convergence and the approximation order of some Durrmeyer type operators in exponential weighted space. Furthermore, we obtain the Voronovskaya type theorem for these operators.

On a generalized [lambda]-Gauss Weierstrass singular integral

Aral A.

Fasciculi Mathematici

2005

Nr 35

23-33

In the present note we consider the integral where x należy Rn, s> 0. and Labda1, Labda2,...Labda n are positive numbers with /Labda/ = Labda 1+Labda 2 + ... + Labdan. The integrals Ws(f; x, Alfa) will be called a generalized A—Gauss Weierstrass singular integral. We study some approximation properties of this integral in the nonisotropic exponential weighted space.

Approximation properties of certain modified Szasz-Mirakyan operators of functions of two variables

Walczak Z.

Fasciculi Mathematici

2004

Nr 34

129-140

We introduce certain modified Szasz-Mirakyan operators in polynomial and exponential weighted spaces of functions of two variables and we study the degree of approximation of functions by these operators.

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.