Mastroianni, Giuseppe; Totik, Vilmos Best approximation and moduli of smoothness for doubling weights. (English) Zbl 0981.41016 J. Approximation Theory 110, No. 2, 180-199 (2001). 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. Reviewer: S.M.Mazhar (Kuwait) Cited in 1 ReviewCited in 21 Documents MSC: 41A50 Best approximation, Chebyshev systems 41A10 Approximation by polynomials 41A25 Rate of convergence, degree of approximation Keywords:doubling weights; moduli of smoothness PDFBibTeX XMLCite \textit{G. Mastroianni} and \textit{V. Totik}, J. Approx. Theory 110, No. 2, 180--199 (2001; Zbl 0981.41016) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.