In this note,we develop,without assuming the Haar condition,a generalized simultaneousChebyshev approximation theory which is similar to the classical Chebyshev
The multivariate splines which were first presented by deBooor as a complete theoreticalsystem have intrigued many mathematicians who have devoted many works in
The following theorem is provedTheorem 1.Let q be a polynomial of degree n(qP<sub>n</sub>)with n distinct zeroes lying inthe interval[-1,1] and△’<sub>q</sub>={-
Let g∈C<sup>q</sup>[-1, 1] be such that g<sup>(k)</sup>(±1)=0 for k=0,…,q. Let P<sub>n</sub> be an algebraic polynomialof degree at most n, such that P<sub>n