Theorem of coincidence of classes for a generalised shift operator

TL;DR

This paper proves a theorem showing the equivalence of function classes defined by best polynomial approximation and generalized Lipschitz conditions via a generalized shift operator.

Contribution

It establishes a coincidence theorem for classes of functions related to a generalized shift operator, extending previous approximation theory results.

Findings

Coincidence of approximation classes proven

Equivalence of polynomial approximation and Lipschitz classes

Extension of classical approximation theorems

Abstract

In this paper, for a generalised shift operator introduced earlier, we prove theorem of coincidence of classes of functions defined by the order of best approximation by algebraical polynomials and the generalised Lipschitz classes defined by the generalised shift operator.