A Study of Weighted Polynomial Approximations with Several Variables (II)
, PP. 1239-1256 10.4236/am.2017.89093
Keywords: Weighted Polynomial Approximations, the Lagrange Interpolation, the Best of Approximation, Inequalities
In this paper we investigate weighted polynomial approximations with several
variables. Our study relates to the approximation for
polynomial. Then we will give some results relating to the Lagrange interpolation,
the best approximation, the Markov-Bernstein inequality and the Nikolskii-
[ 1] Jung, H.S. and Sakai, R. (2009) Specific Examples of Exponential Weights. Communications of the Korean Mathematical Society, 24, 303-319.
[ 2] Levin, A.L. and Lubinsky, D.S. (2001) Orthogonal Polynomials for Exponential Weights. Springer, New York. https://doi.org/10.1007/978-1-4613-0201-8
[ 3] Sakai, R. and Suzuki, N. (2013) Mollification of Exponential Weights and Its Application to the Markov-Bernstein Inequality. The Pioneer Journal of Mathematics, 7, 83-101.
[ 4] Sakai, R. A Study of Weighted Polynomial Approximations with Several Variables (I). Applied Mathematics. (Unpublished)
[ 5] Timan, A.F. (1963) Theory of Approximation of Functions of a Real Variable. Pergamon Press, Oxford.
[ 6] Mhaskar, H.N. (1996) Introduction to the Theory of Weighted Polynomial Approximation. World Scientific, Singapore.
[ 7] Sakai, R. (2015) Quadrature Formula with Exponential-Type Weights. Pioneer Journal of Mathematics and Mathematical Sciences, 14, 1-23.
[ 8] Jung, H.S. and Sakai, R. (2016) Lp-Convergence of Lagrange Interpolation Polynomials with Regular Symmetric Exponential Type Weight. Global Journal of Pure and Applied Mathematics, 12, 797-822.