Hermite–Hadamard Inequalities for a New Riemann–Liouville-Type Operator

Fractal and Fractional 2026 Open access

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Authors: Rubayyi T. Alqahtani, Mehmet Zeki Sarıkaya, Nadiyah Hussain Alharthi
DOI: 10.3390/fractalfract10030147
Cited by: 3
References: 10

Abstract

We introduce a new class of fractional remainder operators, denoted by Rα,nξ+ and Rα,nη−, which generalize and unify various classical integral identities. Using these operators, we formulate refined Hermite–Hadamard and trapezoidal inequalities for differentiable functions. The novelty of our approach lies in its symmetric kernel structure, which facilitates tighter error bounds. Numerical examples are given, including applications to non-differentiable convex functions, to demonstrate the applicability and limitations of the derived results.

Fields of Study & Subjects

Mathematical Inequalities and Applications Approximation Theory and Sequence Spaces Mathematical functions and polynomials

Publication details

Journal / source
Fractal and Fractional
Publisher
MDPI AG
Volume
10
Issue
3
Pages
147–147
Publication date
26 February 2026
Language
EN