NEGATIVE THEOREM FOR LP,0<P<1 MONOTONE APPROXIMATION
DOI:
https://doi.org/10.31642/JoKMC/2018/040301Keywords:
Monotone approximation, algebraic polynomial, best approximation.Abstract
For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: (2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_p≤c〖E_n (f Ì )〗_p, where 〖E_(n+1)^1 (f)〗_p is the degree of the best Lp monotone approximation of the function f by algebraic polynomial of degree not exceeding n+1. 〖E_n (f Ì )〗_p is the degree of the best Lp approximation of the function f Ì by algebraic polynomial of degree not exceeding n.Downloads
References
. E. S. Bhaya, On the constrained and unconstrained approximation, Ph.D. Thesis, University of Baghdad, 2003.
. G. G. Lorentz and K. L. Zeller, Degree of approximation bymonotone polynomials, I, J. Approx. Theory 1(4), (1968), 501-504. DOI: https://doi.org/10.1016/0021-9045(68)90039-7
. R. A. DeVore and G. G. Lorentz, ``Constructive approximation,'' Springer-Verlag, New York, 1993. DOI: https://doi.org/10.1007/978-3-662-02888-9
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Copyright (c) 2017 GHAZI ABDULLAH Madlol
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