Approximation by a special de la Vall\'ee Poussin type matrix transform mean of Walsh-Fourier series

Abstract

In this paper, we consider norm convergence for a special matrix-based de la Vall\'ee Poussin-like mean of Fourier series for the Walsh 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.