FRACTIONAL HERMITE-HADAMARD INEQUALITY AND ERROR ESTIMATES FOR SIMPSON'S FORMULA THROUGH CONVEXITY WITH RESPECT TO A PAIR OF FUNCTIONS

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

MISKOLC MATHEMATICAL NOTES, cilt.24, sa.2, ss.553-568, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.18514/mmn.2023.4214
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.553-568
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this article, we establish two new and different versions of fractional HermiteHadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Ho & BULL;lder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.