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.
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