On extensions and applications of the Beesack inequality for bounding Riemann-Stieltjes integrals

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 (...

Riemann-Stieltjes integrals

This short note gives an introduction to the Riemann-Stieltjes integral on R and Rn. Some natural and important applications in probability theory are discussed. The reason for discussing the Riemann-Stieltjes integral instead of the more general Lebesgue and LebesgueStieltjes integrals are that most applications in elementary probability theory are satisfactorily covered by the Riemann-Stieltj...

Cauchy-stieltjes and Riemann-stielt Jes Integrals

A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces

We prove an inequality of the Loéve-Young type for the Riemann-Stieltjes integrals driven by irregular signals attaining their values in Banach spaces, and, as a result, we derive a new theorem on the existence of the Riemann-Stieltjes integrals driven by such signals. Also, for any [Formula: see text], we introduce the space of regulated signals [Formula: see text] ([Formula: see text] are rea...

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