On error of interval quadrature formula of rectangles for the class $W^2 H_1^{\omega}$

We found the error of interval quadrature formula of rectangles for the class of functions with given convex majorant of integral modulus of continuity of second derivative.

On the best interval quadrature formula for the class $W^2 H_1^{\omega}$

We prove that the rectangular interval quadrature formula is the best for the class of functions with given convex majorant of integral modulus of continuity of the second derivative.

On exact solution of some extremal problems on classes of functions defined by majorant of integral modulus of continuity

The error of the interval quadrature rectangle formula on the class of periodic functions with convex majorant of the integral modulus of continuity of even derivative are obtained.

On trigonometric approximation of functions in the Lq norm

In this paper we obtain a degree of approximation of functions in Lq by operators associated with their Fourier series using integral modulus of continuity. These results generalize many known results and are proved under less stringent conditions on the infinite matrix.