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