On Hermite-Hadamard-Mercer type fractional integral inequalities via a new integral identity

Sinan ASLAN; Sinan ASLAN

doi:10.3934/math.20261338

AIMS Mathematics

2026, Volume 11, Issue 10: 34303-34322. doi: 10.3934/math.20261338

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Research article

On Hermite-Hadamard-Mercer type fractional integral inequalities via a new integral identity

Sinan ASLAN ^,

Agri Turk Telekom Social Sciences High School, Agri, Turkiye

Received: 12 July 2026 Revised: 25 September 2026 Accepted: 10 October 2026 Published: 22 October 2026
MSC : 26A33, 26D15

This study establishes new fractional integral inequalities associated with a certain class of differentiable functions. A composite fractional integral identity is derived by applying the fractional integral identity from Lemma 1 to the subintervals of a uniform partition. This identity serves as the main analytical tool in the subsequent analysis. By systematically combining this identity with Jensen-Mercer, Hölder, power-mean, and Young-type inequalities, several refined Hermite-Hadamard (HH)-type estimates are established. The obtained results extend and unify several existing inequalities reported in the literature while yielding a variety of particular cases through appropriate choices of the parameters.
- Jensen-Mercer,
- fractional integrals,
- Hermite-Hadamard,
- Young inequalities,
- Hölder inequalities
Citation: Sinan ASLAN. On Hermite-Hadamard-Mercer type fractional integral inequalities via a new integral identity[J]. AIMS Mathematics, 2026, 11(10): 34303-34322. doi: 10.3934/math.20261338

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Abstract

This study establishes new fractional integral inequalities associated with a certain class of differentiable functions. A composite fractional integral identity is derived by applying the fractional integral identity from Lemma 1 to the subintervals of a uniform partition. This identity serves as the main analytical tool in the subsequent analysis. By systematically combining this identity with Jensen-Mercer, Hölder, power-mean, and Young-type inequalities, several refined Hermite-Hadamard (HH)-type estimates are established. The obtained results extend and unify several existing inequalities reported in the literature while yielding a variety of particular cases through appropriate choices of the parameters.

References

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