Approximation by Nörlund means with respect to Vilenkin system in Lebesgue spaces

In this paper we improve and complement a result by Móricz and Siddiqi \cite{Mor}. In particular, we prove that their estimate of the Nörlund means with respect to the Vilenkin system holds also without their additional condition. Moreover, we prove a similar approximation result in Lebesgue spaces for any $1\le p<\mathrm{\infty }$.