Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function

  • Arslan Munir
  • , Miguel Vivas-Cortez*
  • , Ather Qayyum
  • , Hüseyin Budak
  • , Irza Faiz
  • , Siti Suzlin Supadi
  • *Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for (Formula presented.) -convex function are obtained. By employing well-known inequalities such as Hölder’s and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.

Original languageEnglish
Pages (from-to)543-566
Number of pages24
JournalMathematical and Computer Modelling of Dynamical Systems
Volume30
Issue number1
DOIs
StatePublished - 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • Euler-Maclaurin-type inequalities
  • corrected Euler-Maclaurin-type inequalities
  • fractional integrals
  • power-mean inequality
  • s-convex function

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