Let there be given finitely many points \(\{\alpha_ k\}^ n_ 1\) from the unit disc. If f is a \(H^ p\)-function then how well can the value of f at \(z=0\) be approximated by linear means \(\sum^{n}_{1}c_ kf(\alpha_ k)?\) We give the optimal constants \(c_ k\) and get, as a corollary, the possibility of the approximation of f by operators of the form \(\sum^{n}_{1}f(\alpha_ k)p_ k\) with polynomials \(p_ k\). The order of approximation depends on the distance \(\sum^{n}_{1}(1- | \alpha_ k|)\) of the point system from the unit circle.