Comonotone Polynomial Approximation in L_p[-1, 1], 0 < p ≤ ∞
نویسندگان
چکیده
Let a function f 2 L p ?1; 1], 0 < p 1 have 1 r < 1 changes of monotonicity. For all suuciently large n, we construct algebraic polynomials p n of degree n which are comonotone with f, and such that kf ? p n k Lp?1; 1] C(r)! ' 2 (f; n ?1) p , where ! ' 2 (f; n ?1) p denotes the Ditzian-Totik second modulus of smoothness in L p metric.
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