On approximation by families of linear polynomial operators in $l_P$-spaces, $0<p<1$

New applications are given for a method of approximation by families of linear polynomial operators in $L_p$-spaces with $0<p<1$ that was developed by the author in previous papers. In particular, a direct theorem and an inverse theorem on approximation 'by angle' of trigonometric polynomials are proved in the case of higher-order moduli of smoothness.