In this paper we shall be concerned with the questions of existence, uniqueness and constructability of those polynomials in k + 1 variables (x1,x2,⋯,xk,y) of degree not greater than ns in xs and m in y which best approximate zero on I1 × I2 ×⋯ × Ik+1, Is = [−1,1], in the Chebyshev sense.
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