Nikolskii-type estimates for coconvex approximation of functions with one inflection point (Q2895242)

Let \(W^rH^\omega _k\) be the subspace of all functions \(f\in C[-1,1]\), possessing an absolutely continuous \((r-1)\)st derivative on \((-1,1)\) and the \(k\)-th modulus of smoothness of which have a \(k\)-majorant function \(\omega \). For each \(r\in N\) the Nikolskii type pointwise estimate for coconvex approximation of functions \(f\in W^rH^\omega _k\), that change their convexity once on \([-1,1]\), are obtained.