Abstract
This chapter investigates generalisations of Integral Inequalities for n-times differentiable mappings. With the aid of the modern theory of inequalities and by the use of a general Peano kernel, explicit bounds for interior point rules are obtained.
Integral equalities are obtained which are then used to develop inequalities for n-times differentiable mappings on the three norms ||·||∞, ||·||ρ and ||·||1· Some particular inequalities are investigated which include explicit bounds for perturbed trapezoid, midpoint, Simpson’s, Newton-Cotes and left and right rectangle rules. The inequalities are also applied to various composite quadrature rules and the analysis allows the determination of the partition required that would assure that the accuracy of the result would be within a prescribed error tolerance.
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Sofo, A. (2002). Integral Inequalities for N—Times Differentiable Mappings. In: Dragomir, S.S., Rassias, T.M. (eds) Ostrowski Type Inequalities and Applications in Numerical Integration. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2519-4_2
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DOI: https://doi.org/10.1007/978-94-017-2519-4_2
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