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 weighted φλ moduli of continuity, where 0≤λ≤1, we bridge the gap between an old result by Fedorov (1983) [4] based on the ordinary modulus of smoothness, and the recent norm estimates implicating the φ modulus of continuity.