BEST APPROXIMATION AND INTEGRAL INTERPOLATION IN THE SPACES OF CONTINUOUS FUNCTIONS

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(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.