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

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

Filomat, vol.40, no.6, pp.1991-2010, 2026 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 40 Issue: 6
  • Publication Date: 2026
  • Doi Number: 10.2298/fil2606991a
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1991-2010
  • Keywords: Fractional integrals, h-Convex functions, Hermite-Hadamard inequalities, Hermite-Hadamard-Mercer inequalities, Jensen-Mercer inequality
  • Kocaeli University Affiliated: Yes

Abstract

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.