Banach Journal of Mathematical Analysis

Generalization of an integral formula of Guessab and Schmeisser

Sanja Kovac and Josip Pecaric

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Weighted version of two-point integral quadrature formula is obtained using $w-$harmonic sequences of functions. Improved version of Guessab and Schmeisser's result is given with new integral inequalities under various regular conditions. As special cases, the generalizations of quadrature formulae of Gauss type are established.

Article information

Banach J. Math. Anal., Volume 5, Number 1 (2011), 1-18.

First available in Project Euclid: 14 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 25D15
Secondary: 65D30: Numerical integration 65D32: Quadrature and cubature formulas

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


Kovac , Sanja; Pecaric, Josip. Generalization of an integral formula of Guessab and Schmeisser. Banach J. Math. Anal. 5 (2011), no. 1, 1--18. doi:10.15352/bjma/1313362975.

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  • A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Theory 115 (2002), no. 2, 260–288.
  • S. Kovač and J. Pečarić, Weighted version of general integral formula, Math.Inequal.Appl. 13 (2010), no. 3, 579–599.
  • S. Kovač, J. Pečarić and A. Vukelić, A generalization of general two-point formula with applications in numerical integration , Nonlinear Anal. 68 (2008), no. 8, 2445–2463.