Approximating classes of functions defined by a generalised modulus of smoothness

Abstract

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.

6 pages, Communicated in the 1st International Eurasian Conference on Mathematics Sciences and Applications (IECMSA), Prishtinë, Kosovo, 2012

References in corpus (2)

• Approximation of classes of functions defined by a generalized $r$-th modulus of smoothness
• Approximating classes of functions defined by operators of differentiation or operators of generalised translation by means of algebraic polynomials