On the best non-symmetric $L_1$-approximations under the constraints on their derivatives

We obtained exact values of the best $L_1$-approximations of classes $W^r_1$ and $W^{r-1}_V$, non-symmetric and one-way $L_1$-approximation of classes $W^r_1$ of periodic functions by splines of order $r$ and $r-1$ with defect 1 and knots at the points $t_j = \frac{2\pi}{n} \left[\frac{j}{2}\right] + (1 - (-1)^j) \frac{h}{2}$, $j\in \mathbb{Z}$ that belong to the class $W^r_1$ and $W^{r-1}_V$.