Approximation of classes of functions defined by a generalized $r$-th modulus of smoothness

Abstract

In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of functions having given order of best approximation by algebraic polynomials.

Cited by in corpus (2)

• Approximating classes of functions defined by operators of differentiation or operators of generalised translation by means of algebraic polynomials
• Direct and inverse theorems of approximation theory for a generalised modulus of smoothness