ON NEW REFINEMENTS AND GENERALIZATIONS OF q-HERMITE-HADAMARD INEQUALITIES FOR CONVEX FUNCTIONS

Alp N., Budak H., Sarikaya M. Z., Ali M. A.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.54, sa.2, ss.361-374, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1216/rmj.2024.54.361
  • Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.361-374
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

We aim to prove generalized estimations for the q-Hermite-Hadamard inequality for convex functions using a parameter. By choosing this particular parameter, we show that our results reduce the previously obtained q-Hermite-Hadamard inequalities. We also present some new refinements of these q-Hermite- Hadamard inequalities. Furthermore, we establish a new lemma and, by using this lemma, we obtain some new quantum inequalities that generalize quantum midpoint and quantum trapezoid inequalities for convex functions.