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

Abstract

In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral ∫abf(t) du (t)$\int_a^b {f(t)} \,du\,(t)$, 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 Lp–Error estimates for the proposed quadrature rules are also obtained.

Keywords

• quadrature formula
• riemann-stieltjes integral
• ostrowski’s inequality
• primary: 41a55
• 65d30
• 65d32