TY - JOUR AU - M. W. Alomari PY - 2013/07/25 Y2 - 2024/03/29 TI - New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann–Stieltjes Integrals and their Applications JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 65 IS - 7 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2476 AB - 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. ER -