Pointwise estimates for polynomial approximation on the semiaxis

We state some pointwise estimates for the rate of weighted approximation of a continuous function on the semiaxis by polynomials. Furthermore we derive matching converse results and estimates involving the derivatives of the approximating polynomials. Using special weighted moduli of continuity, we bridge the gap between an old result by V.M. Fedorov based on the ordinary modulus of smoothness, and the recent norm estimates implicating the Ditzian-Toytik modulus of continuity.