Le règle du trapèze pour l’intégrale de Riemann-Stieltjes. II. (French) Zbl 0565.41030

Let \(a=x_ 0<x_ 1<...<x_ n=b\) be a partition of [a,b] and let g be a given function of bounded variation on [a,b]. The authors give a quadrature formula T(f) for the R-S integral \(\int^{b}_{a}fdg\). This is analogous to the trapezoidal rule and is obtained by replacing f by a piecewise linear interpolant to f on these nodes. Error estimates are also obtained when \(f\in C'[a,b]\). In the second paper, the authors study the same quadrature formula further when f is the primitive of a function of b.v. and when g satisfies a condition (hypothesis H). If g is monotone, they show that the hypothesis H can be realized and that the solution is unique.
Reviewer: A.Sharma


41A55 Approximate quadratures
65D32 Numerical quadrature and cubature formulas


Zbl 0565.41029