A generalized Čebyšev functional 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 (...

A Sharp Bound of the Čebyšev Functional for the Riemann-Stieltjes Integral and Applications

S. S. Dragomir School of Computer Science and Mathematics, Victoria University, P.O. Box 14428, Melbourne, Victoria 8001, Australia Correspondence should be addressed to S. S. Dragomir, [email protected] Received 13 December 2007; Accepted 29 February 2008 Recommended by Yeol Cho A new sharp bound of the Čebyšev functional for the Riemann-Stieltjes integral is obtained. Applications for ...

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.