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

Alomari, M.W.

doi:10.1515/mjpaa-2018-0010

Abstract

In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral $\int_{a}^{b} f (t) d u (t)$ $\int_a^b {f(t)} \,du\,(t)$, 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.

References

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

Abstract

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