Two-Point Quadrature Rules for Riemann-Stieltjes Integrals with Lp-error estimates

Abstract

In this work, we construct a new general two-point quadratre rules for the Riemann--Stieltjes integral ${\int }_a^{b}f\left(t\right)du\left(t\right)$, where the integrand $f$ is assumed to be satisfied with the Hölder condition on $[a,b]$ and the integrator $u$ is of bounded variation on $[a,b]$. The dual formulas under the same assumption are proved. Some sharp error $L^p$--Error estimates for the proposed quadrature rules are also obtained.

19 pages. arXiv admin note: text overlap with arXiv:1812.10674

References in corpus (1)

• New sharp inequalities of Ostrowski and generalized trapezoid type for the Riemann-Stieltjes integrals and applications