| In this paper we obtain a beter answer to Problem 24 of P. Turán [1]: If the Hermite-Fejer interpolation process converges for any f∈ C[-1,1] then the Lagrange interpolation process defined on the same nodes converges for each f with En(f) = o(n-(23)/(18)), where En(f) is the deviation of best uniform approximation of f ∈ C[-1,1] on [-1,1] by polynomials of degree ≤ n. |
