A NEW AND EFFICIENT SIMPSON’S 1/3-TYPE QUADRATURE RULE 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.

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...

Some Grüss Type Inequalities for Riemann-stieltjes Integral and Applications

New Grüss Type Inequalities for Riemann–stieltjes Integral with Monotonic Integrators and Applications

In this paper several new inequalities of Grüss’ type for Riemann– Stieltjes integral with monotonic nondecreasing integrators under various assumptions for integrands are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well. Department of Mathematics, Faculty of Science, Jerash University, 26150 Jerash, Jordan. E-mail address: mwomath@gmail...