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

  • M. W. Alomari Jerash Univ., Jordan

Abstract

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.
Published
25.07.2013
How to Cite
AlomariM. W. “New Sharp Ostrowski-Type Inequalities and Generalized Trapezoid-Type Inequalities for Riemann–Stieltjes Integrals and Their Applications”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 7, July 2013, pp. 894–916, http://umj.imath.kiev.ua/index.php/umj/article/view/2476.
Section
Research articles