AN EFFICIENT FOUR-POINT QUADRATURE SCHEME FOR RIEMANN-STIELTJES INTEGRAL

Relative Convexity and Quadrature Rules for the Riemann–stieltjes Integral

We develop Trapezoid, Midpoint, and Simpson’s rules for the Riemann-Stieltjes integral, the latter two being new. These rules are completely natural when the notion of relative convexity is used. Mathematics subject classification (2010): 65D30.

Two Point Gauss–legendre Quadrature Rule for Riemann–stieltjes Integrals

In order to approximate the Riemann–Stieltjes integral ∫ b a f (t) dg (t) by 2–point Gaussian quadrature rule, we introduce the quadrature rule ∫ 1 −1 f (t) dg (t) ≈ Af ( − √ 3 3 ) + Bf (√ 3 3 ) , for suitable choice of A and B. Error estimates for this approximation under various assumptions for the functions involved are provided as well.

The Riemann-stieltjes Integral on Time Scales

We study the process of integration on time scales in the sense of Riemann-Stieltjes. Analogues of the classical properties are proved for a generic time scale, and examples are given.

Approximating the Riemann-Stieltjes integral by a trapezoidal quadrature rule with applications

In this paper we provide sharp bounds for the error in approximating the Riemann-Stieltjes integral R b a f (t) du (t) by the trapezoidal rule f (a) + f (b) 2 [u (b) u (a)] under various assumptions for the integrand f and the integrator u for which the above integral exists. Applications for continuous functions of selfadjoint operators in Hilbert spaces are provided as well. 1. Introduction I...

A Companion of Ostrowski’s Inequality for the Riemann-stieltjes Integral