Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces

TL;DR

This paper establishes direct and inverse approximation theorems for almost periodic functions within Besicovitch-Stepanets spaces, linking best approximation measures with generalized moduli of smoothness.

Contribution

It introduces new approximation theorems in Besicovitch-Stepanets spaces connecting smoothness and approximation quality.

Findings

Proved direct approximation theorems in $B{ ext{S}}^{p}$ spaces.

Established inverse approximation theorems relating smoothness and approximation.

Linked best approximation measures with generalized moduli of smoothness.

Abstract

Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\mathcal S}^{p}$ of almost periodic functions in terms of the best approximations of functions and their generalized moduli of smoothness.