Estimates for functionals with a known finite set of moments in terms of deviations of operators constructed with the use of the Steklov averages and finite differences
Abstract:
The paper presents a new technique for deriving the estimates mentioned in the title. In particular, this technique allows one to establish Jackson-type inequalities for moduli of continuity of arbitrary order with relatively small constants. The results obtained are valid in different spaces of periodic and nonperiodic functions.
Key words and phrases:best approximation, modulus of continuity, sharp constants, Steklov functions.