We give estimates of approximation by Riesz–Zygmund, Euler and Abel–Poisson means in Stepanets spaces of functions f with finite norm equal to the \(l^p\) -norm of the sequence of Vilenkin–Fourier coefficients ( \(1\leqslant p<\infty \) ) in terms of appropriate K-functional. The Vilenkin systems considered in the paper are of bounded type. For this K-functional instead of modulus of continuity we obtain direct and converse approximation theorems. Also we characterize Lipschitz classes connected with Stepanets spaces and standard modulus of continuity in terms of approximation by cited above means.
