Approximation by matrix transform means with respect to the Walsh system in Lebesgue spaces

TL;DR

This paper extends and generalizes previous results on approximation by matrix transform means in Lebesgue spaces, improving understanding of convergence properties of Walsh system means.

Contribution

It broadens the scope from N"orlund to matrix transform means and from weighted to general matrix means, enhancing theoretical insights into Walsh system approximations.

Findings

Generalization of approximation results to matrix transform means

Extension from weighted to unweighted matrix means

Improved convergence properties in Lebesgue spaces

Abstract

In this paper, we improve, complement and generalize (from N\"or\-lund to matrix transform means) a result of M\'oricz and Siddiqi \cite{MS} and some statements of Areshidze and Tephnadze \cite{AT}, and (from $T$ (weighted) to matrix transform means) Anakidze, Areshidze, Persson and Tephnadze \cite{AAPT}.