On Vallée-Poissin means for special series with respect to ultraspherical Jacobi polynomials with sticking partial sums

This paper continues studying of special series with sticking property ($r$-fold coincidence at points $\pm1$) in ultraspherical Jacobi polynomials, that was started in the works of the first author. Investigation of current paper is paid on approximative properties of Vallée-Poussin means for partial sums of mentioned special series with sticking property. It is shown that for function $f$ with certain smoothness properties at the ends of interval $[-1,1]$ the weighted approximation rate by Vallée-Poussin means has the same order as the best weighted approximation of $f$.