Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with L^p–error estimates

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 L^p–Error estimates for the proposed quadrature rules are also obtained.