New symmetric midpoint type inequalities for convex functions

Hussain R., Gulshan G., Rehman A., Budak H.

FILOMAT, vol.39, no.4, pp.1389-1406, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.2298/fil2504389h
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1389-1406
  • Kocaeli University Affiliated: No

Abstract

In this study, we first develop symmetric quantum integral identity utilizing the derivatives and integrals of symmetric quantum types. Then, by using this identity, we establish modified versions of midpoint-type inequalities for differentiable convex functions. To obtain recent results, a few basic inequalities such as power mean and Holder's, have been utilized. We create links between our results and previous findings in the literature taking q -> 1. For a better understanding and validation of the results, we present numerical results and some graphs. Finally, we provide some examples to illustrate the validity of newly obtained symmetric quantum inequalities. The concepts and methods presented in this work can inspire more investigation.