Alsubaie, N.A, Dragomir, Sever S and Sorrentino, Gabriele ORCID: https://orcid.org/0000-0001-5512-1799 (2026) Three points inequalities for Riemann–Stieltjes integral of Lipschitzian or bounded variation integrands and integrators of r-H Hölder type with applications. Australian Journal of Mathematical Analysis and Applications, 23 (1). ISSN 1449-5910

Abstract

In this paper we obtained some new simple error bounds in approximating the Riemann-Stieltjes integral ^R<inf>a</inf>^b f (t) du(t) by the use of three points rule [u (b) − u ((1 − λ) x + λb)] f (b) + [u(υa + (1 − υ) x) − u (a)]f (a) + [u ((1 − λ) x + λb) − u (υa + (1 − υ) x)] f (x) , where λ, υ ∈ [0, 1], x ∈ [a, b] and assuming that the function f is L-Lipschitzian or of bounded variation and u is r-H-Hölder type on [a, b]. The important case of weighted integrals is considered, compounding quadrature rules are provided and applications for approximation of Fourier transforms on finite intervals are also given.

Search Google Scholar

Repository staff login