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Some new hermite–hadamard and related inequalities for convex functions via (P, q)-integral

  • Miguel Vivas-Cortez
  • , Muhammad Aamir Ali
  • , Hüseyin Budak
  • , Humaira Kalsoom
  • , Praveen Agarwal
  • School of Physical Sciences and Mathematics
  • Nanjing Normal University
  • Duzce University
  • Zhejiang Normal University
  • International College of Engineering
  • International Center for Basic and Applied Sciences

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type inequalities using the notions of (p, q)π2 derivative and (p, q)π2 integral are obtained. Furthermore, for (p, q)π2-differentiable convex functions, some new (p, q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p, q)π2 integral are offered. It is also shown that the newly proved results for p = 1 and q → 1 can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.

Original languageEnglish
Article number828
JournalEntropy
Volume23
Issue number7
DOIs
StatePublished - Jul 2021

Keywords

  • (p, q) estimates for midpoint and trapezoidal type inequalities
  • Post-quantum calculus
  • Quantum calculus

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