Approximation of the Riemann–Liouville Integrals by Algebraic Polynomials on the Segment

The direct approximation theorem by algebraic polynomials is proved for Riemann–Liouville integrals of order $r>0$. As a corollary, we obtain asymptotic equalities for $\varepsilon$-entropy of the image of a Hölder type class under Riemann–Liouville integration operator.