Strong approximation of almost periodic functions

TL;DR

This paper investigates summability methods for almost periodic functions, extending previous results on their approximation by Fourier series using generalized matrix means.

Contribution

It generalizes existing results on strong approximation of almost periodic functions by Fourier series through the introduction of summability methods generated by GM(2b).

Findings

Extended approximation results for almost periodic functions.

Generalized summability methods improve approximation quality.

Built upon and broadened prior theoretical frameworks.

Abstract

We consider summability methods generated by the class GM(2b). We generalize some related results of P. Pych-Taberska [Studia Math. XCVI (1990), 91-103] on strong approximation of almost periodic functions by their Fourier series and S. M. Mazhar and V. Totik [J. Approx. Theory, 60(1990), 174-182] on approximation of periodic functions by matrix means of their Fourier series.