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Research Article | Open Access

Some new $(k, r)$ -Riemann-Liouville fractional Hermite-Hadamard-type inequalities for strongly modified $(α, h - m) - p$ -convex functions

Ayşe Kübra Demirel(

)

Department of Mathematics, Ordu University, Ordu, Türkiye

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Abstract

In this paper, a strongly modified $(α, h - m) - p$ -convex function, which is a class of strongly convex functions, was defined, and the properties of this function were proved. Initially, the Hermite-Hadamard type inequality was proved for the presented function class. Then, the Hermite-Hadamard type inequality was obtained for the $(k, r)$ -Riemann-Liouville fractional integrals. Also, some examples were included. The results were generalizations of various results in the literature.

Keywords

strongly modified (α, h − m) − p-convexity fractional integrals Riemann-Liouville integrals Hermite-Hadamard inequality integral inequalities

CLC number: 26A51, 26B25, 26D15, 33E12

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AIMS Mathematics

Volume 11 Issue 5,
May 2026

Pages 12674-12686

DOI: 10.3934/math.2026521

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Cite this article:

Demirel AK. Some new

(k, r)

-Riemann-Liouville fractional Hermite-Hadamard-type inequalities for strongly modified

(α, h - m) - p

-convex functions. AIMS Mathematics, 2026, 11(5): 12674-12686. https://doi.org/10.3934/math.2026521

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Received: 16 February 2026

Revised: 15 April 2026

Accepted: 21 April 2026

Published: 15 May 2026

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)

Some new ( k , r )-Riemann-Liouville fractional Hermite-Hadamard-type inequalities for strongly modified ( α , h − m ) − p-convex functions

Abstract

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Review Comment

Some new $(k, r)$ -Riemann-Liouville fractional Hermite-Hadamard-type inequalities for strongly modified $(α, h - m) - p$ -convex functions