Geodesic
Approximation of Functions by Polynomials in C[-L, 1]
Canadian journal of mathematics, Tome 44 (1992) no. 5, pp. 924-940

Voir la notice de l'article provenant de la source Cambridge University Press

A pointwise estimate for the rate of approximation by polynomials , For 0 ≤ ƛ ≤ 1, integer r, and δn(x) = n-1 + φ(x), is achieved here. This formula bridges the gap between the classical estimate mentioned in most texts on approximation and obtained by Timan and others (ƛ = 0) and the recently developed estimate by Totik and first author (ƛ = 1 ). Furthermore, a matching converse result and estimates on derivatives of the approximating polynomials and their rate of approximation are derived. These results also cover the range between the classical pointwise results and the modern norm estimates for C[— 1,1].
DOI : 10.4153/CJM-1992-057-2
Mots-clés : 41A25, 41A27, Polynomial approximation, direct and converse results 
Ditzian, Z.; Jiang, D. Approximation of Functions by Polynomials in C[-L, 1]. Canadian journal of mathematics, Tome 44 (1992) no. 5, pp. 924-940. doi: 10.4153/CJM-1992-057-2
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[1] 1. DeVore, R., Lp[—1,1] approximation by algebraic polynomials, linear spaces and approximation, (ed. R Butzer, L. and Nagy, B.Sz), Birkhauser Verlag, Basel, 1978, 397–406. Google Scholar

[2] 2. Ditzian, Z., On interpolation ofLp[a, b] and weighted Sobolev spaces, Pacific J. Math. 90(1980), 307–323. Google Scholar

[3] 3. Ditzian, Z., Interpolation theorems on the rate of convergence of Bernstein polynomials, Approximation Theory III, (ed. Cheney, E.W.), Academic Press, 1980, 341–347. Google Scholar

[4] 4. Ditzian, Z. and Totik, V., Moduli of Smoothness, Springer-Verlag, 1987. Google Scholar

[5] 5. Lorentz, G.G., Approximation of Functions, Holt, Rinehart and Winston, 1966, reprinted by Chelsea, 1988. Google Scholar

[6] 6. Motornii, V.P., Approximation of functions by algebraic polynomials in Lp metric (Russian), Izv. Akad. Nauk. SSSR, 35(1971), 874–899. Google Scholar

[7] 7. Timan, A.F., Theory of functions of a real variable, English translation 1963, Pergamon Press, The MacMillan Co., Russian original published in Moscow by Fizmatgiz in 1960. Google Scholar

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