2019
Том 71
№ 11

# Alomari M. W.

Articles: 2
Article (Ukrainian)

### New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann–Stieltjes Integrals and their Applications

Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 894–916

We prove new sharp weighted generalizations of Ostrowski-type and generalized trapezoid-type inequalities for Riemann–Stieltjes integrals. Several related inequalities are deduced and investigated. New Simpson-type inequalities are obtained for the $\mathcal{R}\mathcal{S}$ -integral. Finally, as an application, we estimate the error of a general quadrature rule for the $\mathcal{R}\mathcal{S}$ -integral via the Ostrowski–generalized-trapezoid-quadrature formula.

Article (English)

### A companion of Dragomir's generalization of Ostrowski's inequality and applications in numerical integration

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 435-450

\lambda) f(x) - \int^b_a f(t)dt\right]\right| \leq\leq\left[\frac{(b-a)^2}{4}(\lambda^2 + (1 - \lambda)^2) + \left(x - \frac{a + b}{2}\right)^2\right] ||f'||_{\infty} are established. Some sharp inequalities are proved. An application to a composite quadrature rule is provided.