Accurate estimates of deviations of spline approximations to classes of differentiable functions

We derive the approximation on $[0,1]$ of functions $f(x)$ by interpolating spline-functions $s_r(f;x)$ of degree $2r+1$ and defect $r+1$ ($r=1,2,\dots$). Exact estimates for $|f(x)-s_r(f;x)|$ and $\|f(x)-s_r(f;x)\|_C$ on the class $W^mH_\omega$ for $m=1$, $r=1,2,\dots$ and $m=2,3$, $r=2$ for the case of convex $\omega(t)$, are derived.