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In this paper, we improve, complement and generalize (from Nör-lund to matrix transform means) a result of Móricz and Siddiqi \cite{MS} and some statements of Areshidze and Tephnadze \cite{AT}, and (from (weighted) to matrix transform means) Anakidze, Areshidze, Persson and Tephnadze \cite{AAPT}.

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