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Bounds for the Chebyshev functional and corrected four-point quadrature formulae of Euler type

The aim of this paper is to consider some new estimations of the reminder in closed corrected four- point quadrature formulae of Euler type using some inequalities for the Chebyshev functional. In special case, we obtain some new bounds for the corrected Euler–Simpson 3/8 formula. Some new error estimates for the corrected Euler Bullen Simpson 3/8 formula are derived too.

Chebyshev functional ; Grüss inequality ; closed corrected four-point quadrature formulae

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