Perturbed Trapezoid Like Inequalities

Waseem Ghazi Alshanti (Mathematics Department, Al Zaytoonah University of Jordan, Queen Alia Airport St 594, Amman, 11733, Jordan)
Iqbal Mohammad Batiha (Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, 346, United Arab Emirates)
Ahmad Alshanty (Cyber Security Department, Isra University, Amman, 11622, Jordan)
Amjed Zraiqat (Mathematics Department, Al Zaytoonah University of Jordan, Queen Alia Airport St 594, Amman, 11733, Jordan)
Iqbal Hamzah Jebril (Mathematics Department, Al Zaytoonah University of Jordan, Queen Alia Airport St 594, Amman, 11733, Jordan)
Ma’mon Ahmad Abu (Mathematics Department, Al Zaytoonah University of Jordan, Queen Alia Airport St 594, Amman, 11733, Jordan)

Science and Technology Indonesia
Vol. 8 No. 2 (2023): April

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.