On $(h,m)$-Convex Functions and Inequalities

Subscription Access
Articles in Press

Authors

  • Lucas Gómez, Juan E. Nápoles Valdés Department of Mathematics, Universidad Nacional del Nordeste, Corrientes, 3400, Argentina Author

DOI:

https://doi.org/10.5890/DNC.2026.09.012

Abstract

This work explores novel integral inequalities for $(h,m)$-convex functions using key mathematical techniques, including Hölder's, Young's and Power Mean inequalities. By leveraging these classical results, we establish improved bounds and extend Hermite-Hadamard type inequalities. The findings contribute to a deeper understanding of $(h,m)$-convex functions and their role in mathematical analysis. Additionally, we discuss particular cases to emphasize the relevance of our contributions.

References

[1] Nápoles Valdés, J.E., Rabossi, F., and Samaniego, A.D. (2020), Convex functions: Ariadne's thread or Charlotte's spiderweb?, Advanced Mathematical Models and Applications, 5(2), 176-191.

[2] Bayraktar, B. (2020), Some new inequalities of Hermite–Hadamard type for differentiable Godunova–Levin functions via fractional integrals, Konuralp Journal of Mathematics, 8(1), 91-96.

[3] Bohner, M., Kashuri, A., Mohammed, P.O., and Nápoles Valdés, J.E. (2022), Hermite–Hadamard-type inequalities for conformable integrals, Hacettepe Journal of Mathematics and Statistics, 51(3), 775-786.

[4] Delgado, J.G.G., Valdés, J.E.N., and Reyes, E.P. (2021), New Hermite–Hadamard inequalities in the framework of generalized fractional integrals, Annals of the University of Craiova, Mathematics and Computer Science Series, 48(2), 319-327.

[5] Galeano, J., Valdés, J.E.N., and Reyes, E.P. (2023), Concerning the generalized Hermite–Hadamard integral inequality, Sigma Journal of Engineering and Natural Sciences, 41(2), 226-231.

[6] Hadamard, J. (1893), Étude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann, Journal de Mathématiques Pures et Appliquées, 58, 171-215.

[7] Hermite, C. (1883), Sur deux limites d'une intégrale définie, Mathesis, 3, 82.

[8] Mitrinović, D.S. and Lacković, I.B. (1985), Hermite and convexity, Aequationes Mathematicae, 28, 229-232.

[9] Valdes, J.E.N. (2022), A review of Hermite–Hadamard inequality, Partners Universal International Research Journal, 1(4), 98-101.

[10] Mehmood, S., Valdés, J.E.N., Fatima, N., and Aslam, W. (2022), Some integral inequalities via fractional derivatives, Advances in Studies: Euro-Tbilisi Mathematical Journal, 15(3), 31-44.

[11] Mehmood, S., Valdes, J.E.N., Fatima, N., and Shahid, B. (2021), Some new inequalities using conformable fractional integral of order $beta$, Journal of Mathematical Extension, 15(SI-NTFCA), 1-22.

[12] Özdemir, M.E., Butt, S.I., Bayraktar, B., and Nasir, J. (2020), Several integral inequalities for $(alpha, s, m)$-convex functions, AIMS Mathematics, 5(4), 3906-3921.

[13] Bayraktar, B. and Nápoles Valdés, J.E. (submitted), A note on Hermite–Hadamard integral inequality for $(h,m)$-convex modified functions in a generalized framework, Submitted.

[14] Sarikaya, M.Z., Set, E., Yaldiz, H., and Başak, N. (2013), Hermite–Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57, 2403-2407.

[15] Sarikaya, M.Z. and Yildirim, H. (2017), On Hermite–Hadamard type inequalities for Riemann–Liouville fractional integrals, Miskolc Mathematical Notes, 17(2), 1049-1059.

[16] Wang, J., Li, X., and Zhou, Y. (2016), Hermite–Hadamard inequalities involving Riemann–Liouville fractional integrals via s-convex functions and applications to special means, Filomat, 30(5), 1143-1150.

[17] Dragomir, S.S. and Fitzpatrick, S. (1999), The Hadamard inequalities for s-convex functions in the second sense, Demonstratio Mathematica, 32(4), 687-696.

[18] Set, E., Sarikaya, M.Z., Özdemir, M.E., and Yildirim, H. (2014), The Hermite–Hadamard's inequality for some convex functions via fractional integrals and related results, Journal of Applied Mathematics, Statistics and Informatics, 10(2), 69.

[19] Ahmad, B., Alsaedi, A., Kirane, M., and Torebek, B.T. (2019), Hermite–Hadamard, Hermite–Hadamard–Fejér, Dragomir–Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals, Journal of Computational and Applied Mathematics, 353, 120-129.

[20] Khan, K.A., Fatima, S., Nosheen, A., and Mabela, R.M. (2024), New developments of Hermite–Hadamard type inequalities via s-convexity and fractional integrals, Hindawi, 2024, p.1997549.

Article Metrics

Citations 0 Crossref
Scheduled issueSeptember 2026

Usage tracking begins September 1, 2026.

History StatusArticles in Press Scheduled issue

Issue

Section

Research Articles

How to Cite

Valdés, L. G. J. E. N. (2026). On $(h,m)$-Convex Functions and Inequalities. Discontinuity, Nonlinearity, and Complexity, 15(3), 451-461. https://doi.org/10.5890/DNC.2026.09.012