Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals

Fatih Hezenci; Hüseyin Budak

doi:10.33434/cams.1660607

EN

Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals

Abstract

In this paper, some Euler-Maclaurin-type inequalities are established by using $h-$convex functions involving Riemann-Liouville fractional integrals. In precisely, using the properties of $h$-convex functions, we prove new Euler-Maclaurin-type inequalities. In addition, we present some Euler-Maclaurin-type inequalities for Riemann-Liouville fractional integrals by using Hölder inequality. Moreover, some Euler-Maclaurin-type inequalities are established by using power-mean inequality. Finally, by using the special choices of the obtained results, we obtain some Euler-Maclaurin-type inequalities.

Keywords

Convex functions, Fractional calculus, Maclaurin, Quadrature formula

References

[1] S. Varosanec, On h-convexity, J. Math. Anal. Appl., 326(1) (2007), 303-311. https://doi.org/10.1016/j.jmaa.2006.02.086
[2] D. S. Mitrinovic, J. E. Pečarić, A. M. Fink, Classical and New Inequalities in Analysis, Springer, Dordrecht, 1993.
[3] W. W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Räumen, Publ. Inst. Math., 23(37) (1978), 13-20.
[4] C. E. M. Pearce, A. M. Rubinov, P-functions, quasi-convex functions and Hadamard-type inequalities, J. Math. Anal. Appl., 240(1) (1999), 92-104. https://doi.org/10.1006/jmaa.1999.6593
[5] I. Iscan, New refinements for integral and sum forms, J. Inequal. Appl., 2019 (2019), Article ID 304, 11 pages. https://doi.org/10.1186/s13660-019-2258-5
[6] R. Gorenflo, F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, Springer Verlag, Wien, 1997.
[7] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
[8] S. S. Dragomir, On Simpson’s quadrature formula for mappings of bounded variation and applications, Tamkang J. Math., 30(1) (1999), 53-58. https://doi.org/10.5556/j.tkjm.30.1999.4207
[9] U. S. Kirmaci, On some Bullen-type inequalities with the kth power for twice differentiable mappings and applications, J. Inequal. Math. Anal., 1(1) (2025), 47-64. https://doi.org/10.63286/jima.2025.04
[10] J. Park, On Simpson-like type integral inequalities for differentiable preinvex functions, Appl. Math. Sci., 7(121) (2013), 6009-6021. http://dx.doi.org/10.12988/ams.2013.39498

[11] P. J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York-San Francisco-London, 1975.
[12] S. Erden, S. Iftikhar, P. Kumam, M. U. Awan, Some Newton’s like inequalities with applications, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM, 114 (2020), Article ID 195, 13 pages. https://doi.org/10.1007/s13398-020-00926-z
[13] S. Gao, W. Shi, On new inequalities of Newton’s type for functions whose second derivatives absolute values are convex, Int. J. Pure Appl. Math., 74(1) (2012), 33-41.
[14] S. Iftikhar, P. Kumam, S. Erden, Newton’s-type integral inequalities via local fractional integrals, Fractals, 28(3) (2020), Article ID 2050037. https://doi.org/10.1142/S0218348X20500371
[15] M. A. Noor, K. I. Noor, S. Iftikhar, Newton inequalities for p-harmonic convex functions, Honam Math. J., 40(2) (2018), 239-250. https://dx.doi.org/10.5831/HMJ.2018.40.2.239
[16] Lj. Dedić, M. Matić, J. Pečarić, Euler-Maclaurin formulae, Math. Inequal. Appl., 6(2) (2003), 247–275.
[17] Lj. Dedić, M. Matić, J. Pečarić, A. Vukelic, On Euler-Simpson 3/8 formulae, Nonlinear Stud., 18(1) (2011), 1-26.
[18] F. Hezenci, H. Budak, Maclaurin-type inequalities for Riemann-Liouville fractional integrals, Ann. Univ. Mariae Curie-Skłodowska Sect. A Math., 76(2) (2022), 15-32. http://dx.doi.org/10.17951/a.2022.76.2.15-32
[19] F. Hezenci, Fractional inequalities of corrected Euler-Maclaurin-type for twice-differentiable functions, Comput. Appl. Math., 42 (2023), 1-15, Article ID 92. https://doi.org/10.1007/s40314-023-02235-8
[20] F. Hezenci, Fractional Maclaurin-type inequalities for twice-differentiable functions, Rocky Mountain J. Math., 55(1) (2025), 155-165. https://doi.org/10.1216/rmj.2025.55.155
[21] I. Franjic, J. Pečarić, I. Perić, A. Vukelić, Euler Integral Identity, Quadrature Formulae and Error Estimations, Element, Zagreb, 2011.
[22] J. E. Pečarić, F. Proschan, Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
[23] M. Gümüş, F. Hezenci, H. Budak, Some new approaches to fractional Euler–Maclaurin-Type inequalities via various function classes, Fractal Fract., 8(7) (2024), Article ID 372, 19 pages. https://doi.org/10.3390/fractalfract8070372

Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Fatih Hezenci ^*
0000-0003-1008-5856
Türkiye

Hüseyin Budak
0000-0001-8843-955X
Türkiye

Early Pub Date

June 14, 2025

Publication Date

July 1, 2025

Submission Date

March 18, 2025

Acceptance Date

May 5, 2025

Published in Issue

Year 2025 Volume: 8 Number: 2

DOI

https://doi.org/10.33434/cams.1660607

IZ

https://izlik.org/JA76ZA33ZF

APA

Hezenci, F., & Budak, H. (2025). Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals. Communications in Advanced Mathematical Sciences, 8(2), 57-69. https://doi.org/10.33434/cams.1660607

AMA

1.Hezenci F, Budak H. Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals. Communications in Advanced Mathematical Sciences. 2025;8(2):57-69. doi:10.33434/cams.1660607

Chicago

Hezenci, Fatih, and Hüseyin Budak. 2025. “Euler-Maclaurin-Type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals”. Communications in Advanced Mathematical Sciences 8 (2): 57-69. https://doi.org/10.33434/cams.1660607.

EndNote

Hezenci F, Budak H (July 1, 2025) Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals. Communications in Advanced Mathematical Sciences 8 2 57–69.

IEEE

[1]F. Hezenci and H. Budak, “Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals”, Communications in Advanced Mathematical Sciences, vol. 8, no. 2, pp. 57–69, July 2025, doi: 10.33434/cams.1660607.

ISNAD

Hezenci, Fatih - Budak, Hüseyin. “Euler-Maclaurin-Type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals”. Communications in Advanced Mathematical Sciences 8/2 (July 1, 2025): 57-69. https://doi.org/10.33434/cams.1660607.

JAMA

1.Hezenci F, Budak H. Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals. Communications in Advanced Mathematical Sciences. 2025;8:57–69.

MLA

Hezenci, Fatih, and Hüseyin Budak. “Euler-Maclaurin-Type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals”. Communications in Advanced Mathematical Sciences, vol. 8, no. 2, July 2025, pp. 57-69, doi:10.33434/cams.1660607.

Vancouver

1.Fatih Hezenci, Hüseyin Budak. Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals. Communications in Advanced Mathematical Sciences. 2025 Jul. 1;8(2):57-69. doi:10.33434/cams.1660607

The published articles in CAMS are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License..

Abstract

Euler-Maclaurin-type Inequalities for $h-$convex Functions via Riemann-Liouville Fractional Integrals

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite