A note on an inverse theorem for a generalised modulus of smoothness

TL;DR

This paper proves an inverse theorem related to Jackson's theorem, involving a generalized modulus of smoothness and an asymmetric translation operator, advancing the theoretical understanding of approximation theory.

Contribution

It establishes a converse to Jackson's theorem for a generalized modulus of smoothness using an asymmetric translation operator, extending classical approximation results.

Findings

Proves a converse theorem for a generalized modulus of smoothness.

Uses an asymmetric operator of generalized translation.

Extends classical approximation theory results.

Abstract

We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.