On Jackson's theorem for the modulus of smoothness determined by a nonsymmetric generalised shift operator

Abstract

In this paper a class of asymmetrical operators of generalised translation is introduced, for each of them generalised moduli of smoothness are introduced, and Jackson's and its converse theorems are proved for those moduli. ----- V eto\v{i} rabote rassmatrivaetsya klass sesimmetrichnykh operatorov obobshchenogo sdviga, dlya kazhdogo iz nikh vvoditsya obobshchennye moduli gladkosti i dlya nikh dokazybaetsya teorma Dzheksona i teorema, obratnaya e\v{i}.