A generalization of general two-point formula with applications in numerical integration |
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| Authors: | S Kova? J Pe?ari? A Vukeli? |
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| Institution: | 1. Faculty of Geotechnical Engineering, Vara?din, University of Zagreb, Hallerova aleja 7, 42000 Vara?din, Croatia;2. Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia;3. Faculty of Food Technology and Biotechnology, Department of Mathematics, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia |
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| Abstract: | We derive a general two-point integral quadrature formula using the concept of harmonic polynomials. An improved version of Guessab and Schmeisser’s result is given with new integral inequalities involving functions whose derivatives belong to various classes of functions (Lp spaces, convex, concave, bounded functions). Furthermore, several special cases of polynomials are considered, and the generalization of well-known two-point quadrature formulae, such as trapezoid, perturbed trapezoid, two-point Newton–Cotes formula, two-point Maclaurin formula, midpoint, are obtained. |
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| Keywords: | 26D15 65D30 65D32 |
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