Abstract
Let X_n={x_(nk)}_k~n=1 be a set of real numbers satisfying -1<x_(nn)<…<x_(n1)<1, q', q: 0≤q'≤q be two integers. For a non-negative integer r, we denote by C_[-1,1]~r the set of all the rth continuously differentiable real-valued functions on [-1, 1], and by ∏_r the set of the polynomials of degree at most r. For a given f ∈C_[-1,1]~(q'), we call the only S_N(f, x)∈∏_N (N = (q+1) n-1) satisfying
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