FRACTIONAL HERMITE-HADAMARD INEQUALITY, SIMPSON'S AND OSTROWSKI'S TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH RESPECT TO A PAIR OF FUNCTIONS

Xie J., Ali M. A., Budak H., Feckan M., Sitthiwirattham T.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, cilt.53, sa.2, ss.611-628, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1216/rmj.2023.53.611
  • Dergi Adı: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.611-628
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

We consider the convexity with respect to a pair of functions and establish a Hermite-Hadamard type inequality for Riemann-Liouville fractional integrals. Moreover, we derive some new Simpson's and Ostrowski's type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.