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

Ayşe Kübra Demirel; Ayşe Kübra Demirel

doi:10.3934/math.2026521

AIMS Mathematics

2026, Volume 11, Issue 5: 12674-12686. doi: 10.3934/math.2026521

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

Ayşe Kübra Demirel ^,

Department of Mathematics, Ordu University, Ordu, Türkiye

Received: 16 February 2026 Revised: 15 April 2026 Accepted: 21 April 2026 Published: 08 May 2026
MSC : 26A51, 26B25, 26D15, 33E12

In this paper, a strongly modified $ (\alpha, 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.
- strongly modified $ (\alpha, h-m)-p $-convexity,
- fractional integrals,
- Riemann-Liouville integrals,
- Hermite-Hadamard inequality,
- integral inequalities
Citation: Ayşe Kübra Demirel. Some new $ (k, r) $-Riemann-Liouville fractional Hermite-Hadamard-type inequalities for strongly modified $ (\alpha, h-m)-p $-convex functions[J]. AIMS Mathematics, 2026, 11(5): 12674-12686. doi: 10.3934/math.2026521

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Abstract

In this paper, a strongly modified $ (\alpha, 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.

References

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