Best approximation of functions in $L_p$ by polynomials on affine system

Estimates of the best $L_p$-approximation of functions by polynomials in an affine system (system of dilations and translations), which are similar to well-known estimates due to Ul'yanov and Golubov for approximations in the Haar system, are obtained. An analogue of A. F. Timan and M. F. Timan's inequality is shown to hold under certain conditions on the generating function of the affine system; this analogue fails for the Haar system for $1<p<\infty$.
Bibliography: 10 titles.