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Zbl 1208.41019
Kovač, Sanja; Pečarić, Josip
Generalization of an integral formula of Guessab and Schmeisser. (English)
[J] Banach J. Math. Anal. 5, No. 1, 1-18, electronic only (2011). ISSN 1735-8787/e

The authors consider two-point quadrature formulas with symmetrically distributed nodes for weighted integrals. Using a generalized form of the classical Peano kernel theory, they prove best possible error estimates for such formulas in spaces of differentiable functions with a weighted $L_p$-norm ($1 \le p \le \infty$) whose weight depends on the weight of the original quadrature formula. Some special cases are considered in detail.
[Kai Diethelm (Braunschweig)]

MSC 2000:: *41A55 Approximate quadratures
26D15 Inequalities for sums, series and integrals of real functions
65D30 Numerical integration

Keywords: weight function; w-harmonic sequences of functions; quadrature formula; Gauss formula; Legendre-Gauss; Chebyshev-Gauss; Hermite-Gauss; inequality; sharp constants; best possible constants; two-point quadrature formula

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