We give exact estimations of certain weighted L2-norms of the derivative of polynomial, which have a curved majorant. They are all obtained as applications of special quadrature formulae. 2000 Mathematical Subject Classification: 41A17, 41A05, 41A55, 65D30

Using the concept of majorant sequences (see [4, ch. XXI], [5], [7], [8]) some new inequalities for Walsh polynomials with complex semi-monotone, complex semi-convex, complex monotone and complex convex coefficients are given.

Using the concept of majorant functions, we prove the existence and uniqueness of holomorphic solutions to nonlinear fractional diffusion problems. The analytic continuation of these solutions is studied and the singularity for two cases are posed.

Approximation theorems were formulated for function continuous in the neighborhood of some point x, -∞< x < ∞. Namely, upper bounds obtained approximations by their Gauss-Weierstrass singular operators terms a majorant first- and second-order continuity moduli relevant functions.

In this paper, we study the generalized interpolation problem in class of entire functions exponential type defined by a certain majorant from convergence class.