BEST APPROXIMATION AND INTEGRAL INTERPOLATION IN THE SPACES OF CONTINUOUS FUNCTIONS

(2)积分插值与切比雪夫多项式的最佳逼近。通过数值实验，我们得到了关于拉格朗日插值算子的范数极小值的重要猜想和第二类切比雪夫多项式的一个刻划。(3)获得最佳逼近的一个算法。我们得到了一个用积分切比雪夫系统最佳逼近的算法，如Remez第二算法。(4)用多项式逼近。我们把Jackson的一个定理推广到K维。

(1) Best approximation by integral Chebyshev systems.To consider an algorithm obtaining best approximations, we have investigated and proved results on best approximations by integral Chebyshev systems.(2) Integral interpolation and Chebyshev polynomials.By numerical experiments, we have formed important conjectures on minimum of the norms of the Lagrange interpolation operators and a chracterization of Chebyshev polynomials in the second kind.(3) An algorithm obtaining best approximations.We have ontained an algorithm best approxmations by integral Chebyshev systems like the Remez second algorithm.(4) Approximation by polynomials.We have extended a theorem of Jackson type to K dimensions.