Hermite-Hadamard-Mercer and related inequalities for h-convex functions via ψ-Hilfer operators

Azzouz N., Benaissa B., BUDAK H., Hezenci F.

Filomat, cilt.40, sa.6, ss.1991-2010, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 6
  • Basım Tarihi: 2026
  • Doi Numarası: 10.2298/fil2606991a
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1991-2010
  • Anahtar Kelimeler: Fractional integrals, h-Convex functions, Hermite-Hadamard inequalities, Hermite-Hadamard-Mercer inequalities, Jensen-Mercer inequality
  • Kocaeli Üniversitesi Adresli: Evet

Özet

We prove a fractional Hermite-Hadamard-Mercer inequality via ψ-Hilfer integral operators for the class of h−convex functions, where h is a B-function. Some novel fractional inequalities related to the left and right sides of the Hermite-Hadamard-Mercer inequalities are established for differentiable mappings whose absolute values of the derivatives are h−convex. Moreover, we construct new inequalities for these differentiable functions using Hölder’s inequality.