Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators

Barış Çelik; Erhan Set

Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators

Abstract

Hermite-Hadamard type inequalities play a central role in the study of convexity and its generalizations, providing a fundamental tool for both theoretical analysis and applications. In recent years, fractional integral operators have been widely employed to establish new versions of these inequalities. Among them, the $\psi$-Hilfer-Atangana-Baleanu ($\psi$-HAB) fractional integral operators have attracted attention as a powerful extension of the Atangana-Baleanu and ABK operators, offering a flexible framework to explore generalized convexity classes. In this paper, with the help of the identities proved by Kermausor et al. in \cite{Kermausuor2025}, we obtain some new integral inequalities of Hermite-Hadamard type for the quasi-convex function and the $P$-function, respectively.

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Barış Çelik ^*
Türkiye

Erhan Set
Türkiye

Publication Date

December 29, 2025

Submission Date

October 20, 2025

Acceptance Date

December 25, 2025

Published in Issue

Year 2025 Volume: 11 Number: 1-2

IZ

https://izlik.org/JA73DB52CY

Cite

RIS / Bibtex

APA

Çelik, B., & Set, E. (2025). Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators. Eastern Anatolian Journal of Science, 11(1-2), 32-38. https://izlik.org/JA73DB52CY

AMA

1.Çelik B, Set E. Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators. Eastern Anatolian Journal of Science. 2025;11(1-2):32-38. https://izlik.org/JA73DB52CY

Chicago

Çelik, Barış, and Erhan Set. 2025. “Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators”. Eastern Anatolian Journal of Science 11 (1-2): 32-38. https://izlik.org/JA73DB52CY.

EndNote

Çelik B, Set E (December 1, 2025) Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators. Eastern Anatolian Journal of Science 11 1-2 32–38.

IEEE

[1]B. Çelik and E. Set, “Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators”, Eastern Anatolian Journal of Science, vol. 11, no. 1-2, pp. 32–38, Dec. 2025, [Online]. Available: https://izlik.org/JA73DB52CY

ISNAD

Çelik, Barış - Set, Erhan. “Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators”. Eastern Anatolian Journal of Science 11/1-2 (December 1, 2025): 32-38. https://izlik.org/JA73DB52CY.

JAMA

1.Çelik B, Set E. Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators. Eastern Anatolian Journal of Science. 2025;11:32–38.

MLA

Çelik, Barış, and Erhan Set. “Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators”. Eastern Anatolian Journal of Science, vol. 11, no. 1-2, Dec. 2025, pp. 32-38, https://izlik.org/JA73DB52CY.

Vancouver

1.Barış Çelik, Erhan Set. Fractional Hermite-Hadamard Inequalities for Different Convex Classes Based on $\psi$-Hilfer-Atangana-Baleanu Operators. Eastern Anatolian Journal of Science [Internet]. 2025 Dec. 1;11(1-2):32-8. Available from: https://izlik.org/JA73DB52CY