Testfunctions for quantitative Korovkin theorems in Lp

Quantitative error estimates for the L_p approximation by positive linear operators can be given by using the so-called averaged modulus of smoothness or τ-modulus of first and second order. The approximation error for the three test function e_i, e_i(x)=xⁱ, i=0,1,2 is hereby of special importance. In this paper it is shown that it is possible to give quantitative L_p error estimates where the monomials are replaced by other Tchebychev systems that have certain additional properties.