IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i18p2920-d1481532.html
   My bibliography  Save this article

Upper Bounds for the Remainder Term in Boole’s Quadrature Rule and Applications to Numerical Analysis

Author

Listed:
  • Muhammad Zakria Javed

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan)

  • Muhammad Uzair Awan

    (Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan)

  • Bandar Bin-Mohsin

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Savin Treanţă

    (Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
    Fundamental Sciences Applied in Engineering-Research Center, National University of Science and Technology Politehnica Bucharest, 060042 Bucharest, Romania)

Abstract

In the current study, we compute some upper bounds for the remainder term of Boole’s quadrature rule involving convex mappings. First, we build a new identity for first-order differentiable mapping, an auxiliary result to establish our required estimates. We provide several upper bounds by utilizing the identity, convexity property, and bounded property of mappings and some well-known inequalities. Moreover, based on our primary findings, we deliver applications to the means, quadrature rule, special mappings, and non-linear analysis by developing a novel iterative scheme with cubic order of convergence. To the best of our knowledge, the current study is the first attempt to derive upper bounds for Boole’s scheme involving convex mappings.

Suggested Citation

  • Muhammad Zakria Javed & Muhammad Uzair Awan & Bandar Bin-Mohsin & Savin Treanţă, 2024. "Upper Bounds for the Remainder Term in Boole’s Quadrature Rule and Applications to Numerical Analysis," Mathematics, MDPI, vol. 12(18), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2920-:d:1481532
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/18/2920/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/18/2920/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Artion Kashuri & Pshtiwan Othman Mohammed & Thabet Abdeljawad & Faraidun Hamasalh & Yuming Chu, 2020. "New Simpson Type Integral Inequalities for - Convex Functions and Their Applications," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2920-:d:1481532. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.