Sahand Communications in Mathematical Analysis

On $m$-Exponential Convexity with Respect to $s$ and Its Applications

Document Type : Research Paper

Author

Nemanja Vučićević

Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Kragujevac, Serbia.

https://doi.org/10.22130/scma.2025.2073121.2349
Abstract
The concept of convexity represents one of the fundamental notions of mathematical analysis and optimization. Various extensions of the concept of convexity have contributed to a wide range of applications, including the study of integral inequalities, approximation theory and other areas of applied mathematics. In this paper, we start from exponentially convex functions defined with respect to $s$ and introduce a new class of $m$-exponentially convex functions with respect to $s$. Furthermore, the basic algebraic properties of this class are analyzed. In the second part, special attention is devoted to the application and the meaning of the extension of the Hermite–Hadamard inequality, where a more general framework is provided compared to the existing ones. The obtained results, in addition to their theoretical significance, also point to the potential for applications in data analysis, optimization and further generalizations.

Keywords

Convexity, m-exponential convexity, Hermite&ndash
Hadamard inequality

Subjects

1. G.A. Anastassiou, Generalised fractional Hermite-Hadamard inequalities involving m-convexity and (s,m)-convexity, Facta Univ., Ser. Math. Inf., 28 (2) (2013), pp. 107-126.
2. M. Avcı Ardıç, A.O. Akdemir and E. Set, On new integral inequalities via geometric-arithmetic convex functions with applications, Sahand Commun. Math. Anal., 19 (2) (2022), pp. 1-14.
3. S.I. Butt, A. Kashuri and J. Nasir, Hermite–Hadamard type inequalities via new exponential type convexity and their applications, Filomat, 35 (6) (2021), pp. 1803-1822.
4. H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1) (1994), pp. 100-111.
5. B.B. Jaimini, Meenu, S.D. Purohit and D.L. Suthar, On the Generalized Class of Multivariable Humbert‐Type Polynomials, Int. J. Math. Math. Sci., 2025 (1) (2025), pp. 1-11.
6. M. Kadakal, Exponential Convex Functions with Respect to s, Sahand Commun. Math. Anal., 21 (2) (2024), pp. 275-287.
7. M. Kadakal, I. Işcan and H. Kadakal, Some new integral inequalities for exponential type P-functions, An. Univ. Craiova, Ser. Mat. Inf., 51 (2) (2024), pp. 291-302.
8. M. Kadakal,I. Işcan, P. Agarwal and M. Jleli, Exponential trigonometric convex functions and Hermite-Hadamard type inequalities, Math. Slovaca, 71 (1) (2021), pp. 43-56.
9. M. Kadakal and I. Işcan, Exponential type convexity and some related inequalities, J. Inequal. Appl., 82 (1) (2020), pp. 1-9.
10. A. Kashuri, S. Iqbal, S.I. Butt, J. Nasir, K.S. Nisar and T. Abdeljawad, Trapezium‐Type Inequalities for k‐Fractional Integral via New Exponential‐Type Convexity and Their Applications, J. Math., 2020 (1) (2020), pp. 1-12.
11. A. Munir, H. Budak, A. Kashuri, I. Faiz, H. Kara and A.Q. Qayyum, Some New Improvements of Hermite-Hadamard Type Inequalities Using Strongly (s,m)-Convex Function with Applications, Sahand Commun. Math. Anal., 22 (2) (2025), pp. 307-332.
12. G. Murugusundaramoorthy, K. Vijaya, S.D. Purohit, Shyamsunder and D.L. Suthar, Initial Coefficient Estimates for Bi‐Univalent Functions Related to Generalized Telephone Numbers, J. Math., 2024 (1) (2024), pp. 1-10.
13. S. Panwar, R.M. Pandey, P. Rai, S.D. Purohit and D.L. Suthar, Hermite–Hadamard-Mercer’s Type Inequalities for ABK-Fractional Integrals via Strong Convexity and its Applications, Discontin. Nonlinearity Complex., 13 (04) (2024), pp. 663-674.
14. X. Qiang, G. Farid, J. Pečarić and S.B. Akbar, Generalized fractional integral inequalities for exponentially (s, m)-convex functions, J. Inequal. Appl., 2020 (1) (2020), pp. 1-13.
15. S. Rashid, F. Safdar, A.O. Akdemir, M.A. Noor and K.I. Noor, Some new fractional integral inequalities for exponentially m-convex functions via extended generalized Mittag-Leffler function, J. Inequal. Appl., 2019 (1) (2019), pp. 1-17.
16. M. Samraiz, K. Saeed, G. Rahman and S. Naheed, Quantum Calculus-Based Error Estimations in Hermite-Hadamard Type Inequalities, Sahand Commun. Math. Anal., 22 (2) (2025), pp. 91-108.
17. M. Samraiz, A. Saleem and S. Naheed, Fractional integral inequalities for m-polynomial exponential type s-convex functions, Filomat, 39 (4) (2025), pp. 1373-1388.
18. S. Özcan, Hermite–Hadamard type inequalities for m-convex and (α,m)-convex functions,, J. Inequal. Appl., 2020 (1) (2020), pp. 1-10.
19. S. Özcan, Hermite-Hadamard type inequalities for exponential type multiplicatively convex functions, Filomat, 37 (28) (2023), pp. 9777-9789.
20. M. Tariq, H. Ahmad, C. Cesarano, H. Abu-Zinadah, A.E. Abouelregal and S. Askar, Novel analysis of hermite–hadamard type integral inequalities via generalized exponential type m-convex functions, Mathematics, 10 (1) (2021), pp. 1-31.
21. S. Toader, The order of a star-convex function, Bull. Applied & Comp. Math., 85 (1998), pp. 347-350.
22. S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m–convex functions, Tamkang J. Math., 33 (1) (2002), pp. 45-56.
Sahand Communications in Mathematical Analysis
Volume 23, Issue 1
Winter 2026
Pages 203-218

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