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Best approximation and moduli of smoothness for doubling weights. (English) Zbl 0981.41016

The authors relate the rate of weighted polynomial approximation to some weighted moduli of smoothness for so-called doubling weights. They also consider the problem in a more restrictive sense for generalized Jacobi weights with zeros in the interval of approximation. These zeros constitute a special problem that has not been resolved so far.

MSC:

41A50 Best approximation, Chebyshev systems
41A10 Approximation by polynomials
41A25 Rate of convergence, degree of approximation
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[1] Griscuolo, G.; Mastroianni, G., Fourier and Lagrange operators in some weighted Sobolev-type space, Acta Sci. Math. (Szeged), 60, 131-146 (1995)
[2] Ditzian, Z.; Totik, V., Moduli of Smoothness. Moduli of Smoothness, Springer Series for Computational Mathematics, 9 (1987), Springer-Verlag: Springer-Verlag New York · Zbl 0666.41001
[3] Mastroianni, G.; Totik, V., Weighted polynomial inequalities with doubling and \(A_∞\) weights, Constr. Approx., 16, 37-71 (2000) · Zbl 0956.42001
[4] Mastroianni, G.; Totik, V., Jackson type inequalities for doubling weights, II, East J. Approx., 5, 101-116 (1999) · Zbl 1084.41510
[5] Mastroianni, G.; Vértesi, P., Weighted \(L_p\) error of Lagrange interpolation, J. Approx. Theory, 82, 321-339 (1995) · Zbl 0828.41001
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