Integration by parts for the generalized 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.

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

Integration by parts with respect to the Henstock-Stieltjes integral in Riesz spaces

Some versions of the formula of integration by parts with respect to the Henstock-Kurzweil and the Henstock-Stieltjes integrals in Riesz spaces are given.

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.

Some Grüss Type Inequalities for Riemann-stieltjes Integral and Applications