On the Best Quadrature Formula of Markov Type for Classes of Functions Defined by Moduli of Continuity

In this paper, for the specified classes of functions defined by moduli of continuity, the extremal problem of finding the best quadrature formula of Markov type is solved. It is proved that the best formula is the classical quadrature formula of trapezoids and its exact error estimate is calculated for the given class of functions. A similar fact is proved for classes of functions defined by the modulus of smoothness, as well as for intermediate classes of functions between the above-mentioned classes of functions defined by the moduli of continuity and moduli of smoothness.