Hermite-Hadamard type inequalities via \((h,m)\)-convexity

Akhtar Abbas; P´eter K´orus; Shahid Mubeen

doi:10.24193/subbmath.2026.1.03

Authors

Akhtar Abbas Department of Mathematics, University of Sargodha, Pakistan; Department of Mathematics, University of Jhang, Pakistan https://orcid.org/0009-0003-6835-6046
P´eter K´orus Institute of Applied Pedagogy, Juh´asz Gyula Faculty of Education, University of Szeged, Hungary https://orcid.org/0000-0001-8540-6293
Shahid Mubeen Department of Mathematics, University of Sargodha, Pakistan; Department of Mathematics, Baba Guru Nanak University, Pakistan https://orcid.org/0000-0002-7815-8516

DOI:

https://doi.org/10.24193/subbmath.2026.1.03

Keywords:

Hermite–Hadamard inequality, fractional integral, convex function, (h,m)-convex functions

Abstract

In this paper, we establish a novel Hermite-Hadamard inequality for \((h,m)\)-convex functions using Riemann--Liouville fractional integral operators, right and left. Furthermore, some new Hermite--Hadamard type fractional integral inequalities are proved for differentiable functions whose first derivative is \((h,m)\)-convex. We demonstrate that these newly established integral inequalities generalize some existing results.

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