Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals

Hüseyin Budak; Hasan Kara; Fatih Hezenci

doi:10.36753/mathenot.1891384

Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals

Abstract

In this investigation, Hermite-Hadamard-type inequalities are acquired forco-ordinated convex functions using generalized fractional integrals. Theseintegrals include several well-known fractional operators, such as theRiemann-Liouville, Hadamard, and Katugampola fractional integrals. Thefindings of this study extend and generalize various inequalities from theexisting literature. Moreover, by choosing specific parameter values, theestablished inequalities reduce to known results as special cases. Inaddition to these generalizations, new inequalities are established. Todemonstrate the applicability of the results, examples are given, andgraphical representations are utilized to support their validity.

Keywords

Co-ordinated convex function, Fractional integral, Hermite-Hadamard type inequalities

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Hüseyin Budak
0000-0001-8843-955X
Türkiye

Hasan Kara ^*
0000-0002-2075-944X
Türkiye

Fatih Hezenci
0000-0003-1008-5856
Türkiye

Early Pub Date

April 11, 2026

Publication Date

-

Submission Date

February 17, 2026

Acceptance Date

March 29, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.36753/mathenot.1891384

IZ

https://izlik.org/JA36WA99DM

APA

Budak, H., Kara, H., & Hezenci, F. (2026). Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals. Mathematical Sciences and Applications E-Notes, Advanced Online Publication, 67-91. https://doi.org/10.36753/mathenot.1891384

AMA

1.Budak H, Kara H, Hezenci F. Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals. Math. Sci. Appl. E-Notes. 2026;(Advanced Online Publication):67-91. doi:10.36753/mathenot.1891384

Chicago

Budak, Hüseyin, Hasan Kara, and Fatih Hezenci. 2026. “Hermite-Hadamard-Type Inequalities for Co-Ordinated Convex Mappings via Generalized Fractional Integrals”. Mathematical Sciences and Applications E-Notes, no. Advanced Online Publication: 67-91. https://doi.org/10.36753/mathenot.1891384.

EndNote

Budak H, Kara H, Hezenci F (April 1, 2026) Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals. Mathematical Sciences and Applications E-Notes Advanced Online Publication 67–91.

IEEE

[1]H. Budak, H. Kara, and F. Hezenci, “Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals”, Math. Sci. Appl. E-Notes, no. Advanced Online Publication, pp. 67–91, Apr. 2026, doi: 10.36753/mathenot.1891384.

ISNAD

Budak, Hüseyin - Kara, Hasan - Hezenci, Fatih. “Hermite-Hadamard-Type Inequalities for Co-Ordinated Convex Mappings via Generalized Fractional Integrals”. Mathematical Sciences and Applications E-Notes. Advanced Online Publication (April 1, 2026): 67-91. https://doi.org/10.36753/mathenot.1891384.

JAMA

1.Budak H, Kara H, Hezenci F. Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals. Math. Sci. Appl. E-Notes. 2026;:67–91.

MLA

Budak, Hüseyin, et al. “Hermite-Hadamard-Type Inequalities for Co-Ordinated Convex Mappings via Generalized Fractional Integrals”. Mathematical Sciences and Applications E-Notes, no. Advanced Online Publication, Apr. 2026, pp. 67-91, doi:10.36753/mathenot.1891384.

Vancouver

1.Hüseyin Budak, Hasan Kara, Fatih Hezenci. Hermite-Hadamard-Type Inequalities for Co-ordinated Convex Mappings via Generalized Fractional Integrals. Math. Sci. Appl. E-Notes. 2026 Apr. 1;(Advanced Online Publication):67-91. doi:10.36753/mathenot.1891384