An inequality for the Riemann-Stieltjes integral

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

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.

Bounding the Cebysev functional for the Riemann-Stieltjes integral via a Beesack inequality and applications

Lower and upper bounds of the μ Cebyšev functional for the RiemannStieltjes integral are given. Applications for the three point quadrature rules of functions that are n time di¤erentiable are also provided. 1. Introduction In 1975, P.R. Beesack [1] showed that, if y; v; w are real valued functions de…ned on a compact interval [a; b] ; where w is of bounded variation with total variation Wb a (...

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.

A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality

Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Loéve-Young inequality for the Riemann-Stieltjes integrals driven by irregular signals. Using this result we strengthen some results of Lyons on the existence of solutions of integral equatio...