Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions

Ali Yılmaz; Abdullah Akkurt; Huseyin Yıldırım

doi:10.47000/tjmcs.1791073

Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions

Abstract

In this study, we introduce a novel definition of convexity in the context of exponential coordinates. Utilizing this new framework, we establish a series of fractional Hermite-Hadamard type inequalities. Furthermore, we provide several remarks to elucidate the connections between our findings and previously established results in the literature.

Keywords

References

Akkurt, A., Sarikaya, M.Z., Budak, H., Yildirim, H., On the Hadamard’s type inequalities for co-ordinated convex functions via fractional integrals, J. King Saud Univ. Sci., 29(2017), 380–387.
Akkurt, A., Sarikaya, M.Z., Budak, H., Yildirim, H., On the Hermite–Hadamard type inequalities for co-ordinated convex functions, Appl. Comput. Math., 20(3)(2021), 408–420.
Azpeitia, A.G., Convex functions and the Hadamard inequality, Rev. Colomb. Math., 28(1994), 7–12.
Bakula, M.K., Peˇcari´c, J., Note on some Hadamard-type inequalities, J. Inequal. Pure Appl. Math., 5(3)(2004), Article 74.
Cumaoğlu, F., Akkurt, A., Yıldırım, H., On the Hadamard’s type inequalities for exponential type co-ordinated convex functions via fractional integrals, in: Advanced Mathematics for the Modeling and Solution of Challenging Problems in Engineering, Springer, 2025, 179–200.
Dragomir, S.S., Pearce, C.E.M., Selected topics on Hermite–Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
Dragomir, S.S., On Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 4(2001), 775–788.
Kadakal, M., İşcan, İ., Exponential-type convexity and some related inequalities, J. Inequal. Appl., 2020(2020), 1–9.

Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations, North-Holland Math. Stud., 204, Elsevier, 2006.
Kırmacı, U.S., Dikici, R., On some Hermite–Hadamard type inequalities for twice differentiable mappings and applications, Tamkang J. Math., 44(1)(2013), 41–51.
Latif, M.A., Dragomir, S.S., On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 1(2012), 1–13.
Miller, S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, 1993.
Muhammedoğlu, A., Akkurt, A., Yıldırım, H., On Hermite–Hadamard type inequalities for co-ordinated convex functions via proportional fractional integrals, in: Advanced Mathematics for the Modeling and Solution of Challenging Problems in Engineering, 13–42, Springer, 2025.
Samko, S.G., Kilbas, A.A., Marichev, O.I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, 1993.
Sarikaya, M.Z., On the Ostrowski-type integral inequality for double integrals, Demon. Math., 45(2012), 533–540.
Sarikaya, M.Z., On the Hermite–Hadamard-type inequalities for co-ordinated convex functions via fractional integrals, Integr. Transf. Spec. Funct., 25(2014), 134–147.
Sarikaya, M.Z., Budak, H., Yaldiz, H., Chebyshev type inequalities for co-ordinated convex functions, Pure Appl. Math. Lett., 2(2014), 36–40.
Sarikaya, M.Z., Budak, H., Yaldiz, H., Some new Ostrowski-type inequalities for co-ordinated convex functions, Turkish J. Anal. Numb. Theory, 2(2014), 176–182.
Sarikaya, M.Z., Some inequalities for differentiable co-ordinated convex mappings, Asian-Eur. J. Math., 8(2015).
Sarikaya, M.Z., Set, E., Özdemir, M.E., Dragomir, S.S., New Hadamard-type inequalities for co-ordinated convex functions, Tamsui Oxford J. Inf. Math. Sci., 28(2012), 137–152.
Sarikaya, M.Z., Set, E., Yaldiz, H., Basak, N., Hermite–Hadamard inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57(2012), 2403–2407.
Sarikaya, M.Z., Yaldiz, H., On the Hadamard’s type inequalities for L-Lipschitzian mappings, Konuralp J. Math., 1(2)(2013), 33–40.

Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Ali Yılmaz
0009-0008-1330-1204
Türkiye

Abdullah Akkurt ^*
0000-0001-5644-1276
Türkiye

Huseyin Yıldırım
0000-0001-8855-9260
Türkiye

Publication Date

February 23, 2026

Submission Date

September 30, 2025

Acceptance Date

November 1, 2025

Published in Issue

Year 2026 Volume: 18 Number: 1

DOI

https://doi.org/10.47000/tjmcs.1791073

IZ

https://izlik.org/JA64JT49JB

Cite

RIS / Bibtex

APA

Yılmaz, A., Akkurt, A., & Yıldırım, H. (2026). Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions. Turkish Journal of Mathematics and Computer Science, 18(1), 95-110. https://doi.org/10.47000/tjmcs.1791073

AMA

1.Yılmaz A, Akkurt A, Yıldırım H. Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions. TJMCS. 2026;18(1):95-110. doi:10.47000/tjmcs.1791073

Chicago

Yılmaz, Ali, Abdullah Akkurt, and Huseyin Yıldırım. 2026. “Fractional Integral Inequalities of Hermite–Hadamard Type for Exponentially Co-Ordinated Convex Functions”. Turkish Journal of Mathematics and Computer Science 18 (1): 95-110. https://doi.org/10.47000/tjmcs.1791073.

EndNote

Yılmaz A, Akkurt A, Yıldırım H (February 1, 2026) Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions. Turkish Journal of Mathematics and Computer Science 18 1 95–110.

IEEE

[1]A. Yılmaz, A. Akkurt, and H. Yıldırım, “Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions”, TJMCS, vol. 18, no. 1, pp. 95–110, Feb. 2026, doi: 10.47000/tjmcs.1791073.

ISNAD

Yılmaz, Ali - Akkurt, Abdullah - Yıldırım, Huseyin. “Fractional Integral Inequalities of Hermite–Hadamard Type for Exponentially Co-Ordinated Convex Functions”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 95-110. https://doi.org/10.47000/tjmcs.1791073.

JAMA

1.Yılmaz A, Akkurt A, Yıldırım H. Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions. TJMCS. 2026;18:95–110.

MLA

Yılmaz, Ali, et al. “Fractional Integral Inequalities of Hermite–Hadamard Type for Exponentially Co-Ordinated Convex Functions”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 95-110, doi:10.47000/tjmcs.1791073.

Vancouver

1.Ali Yılmaz, Abdullah Akkurt, Huseyin Yıldırım. Fractional Integral Inequalities of Hermite–Hadamard type for Exponentially Co-ordinated Convex Functions. TJMCS. 2026 Feb. 1;18(1):95-110. doi:10.47000/tjmcs.1791073