A note on Lagrange interpolation of functions of generalized bounded variation

In this paper we solve a remained problem in 2], whether the following estimate approximation for the classf∈-1, 1]∩BV by Lagrange interpolation based on the Jacobi abscissas: L _n ^(a,d) (f,x)−f(x)=O(1/n) holds, if α≠β α,β≥−1. The project is supported by the Natural Science Foundation of Zhejiang Province.