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Generalized Alomari functionals

2015

We consider a generalized form of certain integral inequalities given by Guessab, Schmeisser and Alomari. The trapezoidal, mid point, Simpson, Newton-Simpson rules are obtained as special cases. Also, inequalities for the generalized Alomari functional in terms of the $n$-th order modulus, $n=\overline{1,4}$, are given and applied to some known quadrature rules.

General Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEsComputer Science::Numerical Analysis01 natural sciencesMidpointModulus of continuityQuadrature (mathematics)Moduli010101 applied mathematicsMathematics::Algebraic Geometry41A44 41A55 41A80 65D30Mathematics - Classical Analysis and ODEsMathematikClassical Analysis and ODEs (math.CA)FOS: MathematicsApplied mathematics0101 mathematicsMathematics
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