On coincidence of classes of functions defined by the generalized modulus of smoothness and appropriate inverse theorem. (English) Zbl 1052.41517

Berisha, Faton M.

Math. Montisnigri 9, 15-36 (1998).

Summary: We prove a theorem of coincidence of the class of functions defined by the generalized modulus of smoothness with the class of functions defined by the order of the best approximation by algebraic polynomials. We also prove the appropriate inverse theorem in approximation theory.

MSC:

41A35	Approximation by operators (in particular, by integral operators)
41A50	Best approximation, Chebyshev systems
42A16	Fourier coefficients, Fourier series of functions with special properties, special Fourier series