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

Rempulska L., Skorupka M.

Fasciculi Mathematici

2005

Nr 35

115-133

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])

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.