Approximating classes of functions defined by a generalised modulus of smoothness. (English) Zbl 1353.41005

Berisha, Faton M.; Berisha, Nimete SH.

Math. Sci. Appl. E-Notes 1, No. 2, 84-89 (2013).

Summary: In the present paper, we use a generalised shift operator in order to define a generalised modulus of smoothness. By its means, we define generalised Lipschitz classes of functions, and we give their constructive characteristics. Specifically, we prove certain direct and inverse types theorems in approximation theory for 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 Lipschitz classes; generalised modulus of smoothness; asymmetric generalised shift operator; theorem of coincidence of classes