New symmetric midpoint type inequalities for convex functions

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

FILOMAT, cilt.39, sa.4, ss.1389-1406, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 4
  • Basım Tarihi: 2025
  • Doi Numarası: 10.2298/fil2504389h
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1389-1406
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

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.