A new version of (<i>p</i>, <i>q</i>)-Hermite-Hadamard's midpoint and trapezoidal inequalities via special operators in (<i>p</i>, <i>q</i>)-calculus

Sitthiwirattham T., Ali M. A., Budak H., Etemad S., Rezapour S.

BOUNDARY VALUE PROBLEMS, vol.2022, no.1, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2022 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1186/s13661-022-01665-3
  • Journal Name: BOUNDARY VALUE PROBLEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Kocaeli University Affiliated: No

Abstract

In this paper, we conduct a research on a new version of the (p, q)-Hermite-Hadamard inequality for convex functions in the framework of postquantum calculus. Moreover, we derive several estimates for (p, q)-midpoint and (p, q)-trapezoidal inequalities for special (p, q)-differentiable functions by using the notions of left and right (p, q)-derivatives. Our newly obtained inequalities are extensions of some existing inequalities in other studies. Lastly, we consider some mathematical examples for some (p, q)-functions to confirm the correctness of newly established results.