Approximation of functions by Borel means of Fourier series with respect to multiplicative systems

In the present paper we consider Borel means of Fourier series with respect to Vilenkin systems with bounded generating sequence and obtain some estimates of approximation by this means in $L^p$, uniform and Hölder type norm in classes of functions with given majorant of best approximation or modulus of continuity. In the trigonometric case similar results were established by P. Chandra, L. Rempulska and K. Tomczak.