Approximating classes of functions defined by operators of differentiation or operators of generalised translation by means of algebraic polynomials. (English) Zbl 1254.41016

Berisha, N. Sh.; Berisha, F. M.

Int. J. Math. Anal., Ruse 6, No. 53-56, 2709-2727 (2012).

Summary: Approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of classes of functions defined by the order of best approximation by algebraic polynomials.

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

Keywords:

generalised modulus of smoothness; asymmetric operator of generalised translation; coincidence of classes; best approximations by algebraic polynomials