Approximation by a special de la Vallée Poussin type matrix transform mean of Vilenkin–Fourier series.

We consider the norm convergence for a special matrix-based de la Vallée Poussin-like mean of Fourier series with respect to the Vilenkin system. We estimate the difference between the named mean above and the corresponding function in norm, and the upper estimation is given by the modulus of continuity of the function. We also give theorems with respect to norm and almost everywhere convergences. [ABSTRACT FROM AUTHOR]