@article{Alomari_2013, title={New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann–Stieltjes Integrals and their Applications}, volume={65}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2476}, abstractNote={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 <span class="a-plus-plus inline-equation id-i-eq1"> <span class="a-plus-plus equation-source format-t-e-x">\( \mathcal{R}\mathcal{S} \)</span> </span>-integral. Finally, as an application, we estimate the error of a general quadrature rule for the <span class="a-plus-plus inline-equation id-i-eq2"> <span class="a-plus-plus equation-source format-t-e-x">\( \mathcal{R}\mathcal{S} \)</span> </span&gt;-integral via the Ostrowski–generalized-trapezoid-quadrature formula.}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Alomari, M. W.}, year={2013}, month={Jul.}, pages={894–916} }