2018/12/01 by Mohammad W. Alomari · 1 citation
Mathematics · #Bounded function #Combinatorics #Fractional Differential Equations Solutions #Integral equation #Mathematical Inequalities and Applications #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Physics #Quadrature (astronomy) #Riemann–Stieltjes integral #math.CA #msc:41A55 #msc:65D30 #msc:65D32
paper · pdf · doi:10.1515/mjpaa-2018-0010
published in Moroccan Journal of Pure and Applied Analysis 4(2), 94-109 (De Gruyter) · 19 pages. arXiv admin note: text overlap with arXiv:1812.10674
openalex publication_date 2018/12/01 · openalex created_date 2019/01/11 · arxiv created 2019/03/15 · arxiv updated 2019/05/24 · openalex updated_date 2026/08/05
Abstract In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:msubsup> <m:mo>∫</m:mo> <m:mi>a</m:mi> <m:mi>b</m:mi> </m:msubsup> <m:mrow> <m:mi>f</m:mi> <m:mo>(</m:mo> <m:mi>t</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mi> </m:mi> <m:mi>d</m:mi> <m:mi>u</m:mi> <m:mi> </m:mi> <m:mo>(</m:mo> <m:mi>t</m:mi> <m:mo>)</m:mo> </m:mrow> </m:math> ∫ab f(t) du (t) , where the integrand f is assumed to be satisfied with the Hölder condition on [ a , b ] and the integrator u is of bounded variation on [ a , b ]. The dual formulas under the same assumption are proved. Some sharp error L p –Error estimates for the proposed quadrature rules are also obtained.