Refinements of the Fractional Hermite-Hadamard Inequality via Arbitrary Means

Authors

  • Mehmet Zeki Sarikaya Düzce University

Keywords:

Hermite-Hadamard inequality, convex functions, Riemann-Liouville fractional integrals, means

Abstract

This paper aims to refine the fractional Hermite-Hadamard inequality by employing arbitrary means defined on a given interval. Using weighted integral techniques and properties of convex functions, new bounds are established that improve upon existing results.

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References

[1] S. S. Dragomir and C. E. M. Pearce. Selected Topics on Hermite-Hadamard Inequalities. RGMIA Monographs, Victoria University, 2000. 1

[2] M. Z. Sarikaya, E. Set, H. Yaldiz, and N. Ba¸sak. Hermite–hadamard’s inequalities for fractional integrals and related

fractional inequalities. Mathematical and Computer Modelling, 57(9-10):2403–2407, 2013. 1, 1

[3] E. Set, ˙I. ˙ I¸scan, M. Z. Sarikaya, and M. E. ¨ Ozdemir. On new inequalities of hermite–hadamard–fej´er type for convex

functions via fractional integrals. Applied Mathematics and Computation, 259:875–881, 2015. 1

[4] S. Simi´c. Further improvements of hermite-hadamard integral inequality. Kragujev. J. Math., 43(2):259–265, 2019. 1, 2.6, 2.8, 2.12

[5] S. Simi´c and B. Bin-Mohsin. Some generalizations of the hermite–hadamard integral inequality. Journal of Inequalities and Applications, 2021(1): 72, 2021.

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Published

2025-09-10

How to Cite

Refinements of the Fractional Hermite-Hadamard Inequality via Arbitrary Means. (2025). Journal of Prime Research in Mathematics, 21(1), 71-81. https://jprm.sms.edu.pk/index.php/jprm/article/view/244