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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])