Perturbed Trapezoid Like Inequalities - Waseem Ghazi Alshanti; Iqbal Mohammad Batiha; Ahmad Alshanty; Amjed Zraiqat; Iqbal Hamzah Jebril; Ma’mon Ahmad Abu (Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya, 2023)
In our current research article, based on a general configuration of a 3-step Peano kernel, new versions of integral inequality of Ostrowski’s type are developed for differentiable mappings that have second derivatives belong to L∞. Then we utilized these versions to generate new perturbed trapezoid like inequalities. These new perturbed trapezoid like inequalities are proposed with error bounds smaller than and similar to those reported by previous studies. Moreover, some of the obtained perturbed trapezoid like inequalities reveal the relationship between the Euler-Maclaurin summation and the trapezoidal rule. Finally, certain implementations to numerical composite quadrature rules are provided for completeness.