Let σ > 0, and let G,B ∈ L(ℝ). This paper is devoted to approximation of convolution classes f = ϕ*G, ϕ ∈ L_p(ℝ), by a space S_B that consists of functions of the form. Under some conditions on G and B, linear operators X_σ,G,B with values in S_B are constructed for which ||f -X_σ,G,B(f)||_p ≤ K_σ,G||ϕ||_p. For p = 1,∞ the constant K_σ,G (it is an analog of the well-known Favard constant) cannot be reduced, even if one replaces the left-hand side by the best approximation by the space S_B. The results of the paper generalize classical inequalities for approximations by entire functions of exponential type and by splines.