References
- M. Andrić and J.E. Pečarić, On (h, g; m)-convexity and the Hermite-Hadamard inequality, J. Convex Anal. 29 (2022), no. 1, 257–268.
- A.J. Aw and N.A. Rosenberg, Bounding measures of genetic similarity and diversity using majorization, J. Math. Biol. 77 (2018), no. 3, 711–737.
- N.S. Barnett, P. Cerone, and S.S. Dragomir, Majorisation inequalities for Stieltjes integrals, Appl. Math. Lett. 22 (2009), no. 3, 416–421.
- A. Belloni, T.Y. Liang, H. Narayanan, and A. Rakhlin, Escaping the local minima via simulated annealing: optimization of approximately convex functions, in: P. Grünwald et al. (eds.), Proceedings of the 28th Conference on Learning Theory, Proc. Mach. Learn. Res., 40, PMLR, 2015, pp. 240–265. Available at arXiv: 1501.07242.
- J.M. Borwein and J.D. Vanderwerff, Convex Functions: Constructions, Characterizations and Counterexamples, Encyclopedia Math. Appl., 109, Cambridge University Press, Cambridge, 2010.
- M. Dehmer and F. Emmert-Streib (eds.), Quantitative Graph Theory: Mathematical Foundations and Applications, CRC Press, Boca Raton, 2015.
- S.J. Dilworth, R. Howard, and J.W. Roberts, Extremal approximately convex functions and estimating the size of convex hulls, Adv. Math. 148 (1999), no. 1, 1–43.
- S.J. Dilworth, R. Howard, and J.W. Roberts, A general theory of almost convex functions, Trans. Amer. Math. Soc. 358 (2006), no. 8, 3413–3445.
- S.S. Dragomir (ed.), Inequalities for Csiszár f-Divergence in Information Theory, RGMIA Monographs, Victoria University, 2000.
- S.S. Dragomir, Hermite-Hadamard type inequalities for MN-convex functions, Aust. J. Math. Anal. Appl. 18 (2021), no. 1, Art. 1, 127 pp.
- S.S. Dragomir and C.E.M. Pearce, Quasi-convex functions and Hadamard’s inequality, Bull. Austral. Math. Soc. 57 (1998), no. 3, 377–385.
- S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
- H.J. Greenberg and W.P. Pierskalla, A review of quasi-convex functions, Operations Res. 19 (1971), no. 7, 1553–1570.
- G.H. Hardy, J.E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, London, 1934.
- D.H. Hyers and S.M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc. 3 (1952), no. 5, 821–828.
- M.A. Khan, S.I. Bradanović, N. Latif, Ð. Pečarić, and J.E. Pečarić, Majorization Inequality and Information Theory. Selected Topics of Majorization and Applications, Monogr. Inequal., 16, ELEMENT, Zagreb, 2019.
- A.R. Khan, J.E. Pečarić, M. Praljak, and S. Varošanec, General Linear Inequalities and Positivity. Higher Order Convexity, Monogr. Inequal., 12, ELEMENT, Zagreb, 2017.
- J.C. Kuang, Applied Inequalities, 4th ed., (in Chinese), Shandong Science and Technology Press, Jinan, 2010.
- T.Y. Li and R.Z. Zhang, Quantum speedups of optimizing approximately convex functions with applications to logarithmic regret stochastic convex bandits, in: S. Koyejo et al. (eds.), NIPS’22: Proceedings of the 36th International Conference on Neural Information Processing Systems, Curran Associates Inc., Red Hook, NY, 2022, Art. no. 228, pp. 3152–3164. Available at arXiv: 2209.12897.
- A.W. Marshall, I. Olkin, and B.C. Arnord, Inequalities: Theory of Majorization and Its Applications, 2nd ed., Springer Ser. Statist., Springer, New York, 2011.
- D.S. Mitrinović, J.E. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Math. Appl. (East European Ser.), 61, Springer Science+Business Media, Dordrecht, 1993.
- K. Mosler, Majorization in economic disparity measures, Linear Algebra Appl. 199 (1994), 91–114.
- C.T. Ng and K. Nikodem, On approximately convex functions, Proc. Amer. Math. Soc. 118 (1993), no. 1, 103–108.
- C.P. Niculescu and L.-E. Persson, Convex Functions and Their Applications, CMS Books Math./Ouvrages Math. SMC, 23, Springer, New York, 2006.
- J.C. Parnami and H.L. Vasudeva, On the stability of almost convex functions, Proc. Amer. Math. Soc. 97 (1986), no. 1, 67–70.
- J.E. Pečarić, On some inequalities for functions with nondecreasing increments, J. Math. Anal. Appl. 98 (1984), no. 1, 188–197.
- J.E. Pečarić, F. Proschan, and Y.L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Math. Sci. Engrg., 187, Academic Press, Inc., Boston, MA, 1992.
- J.E. Pečarić and D. Zwick, n-convexity and majorization, Rocky Mountain J. Math. 19 (1989), no. 1, 303–311.
- J. Ponstein, Seven kinds of convexity, SIAM Rev. 9 (1967), no. 1, 115–119.
- T. Popoviciu, Les Fonctions Convexes, Actualités Sci. Indust., No. 992 [Current Scientific and Industrial Topics], Hermann & Cie, Paris, 1944.
- A. Prékopa, Inequalities for discrete higher order convex functions, J. Math. Inequal. 4 (2009), no. 4, 485–498.
- W.-L. Wang, Approaches to Prove Inequalities, (in Chinese), Harbin Institute of Technology Press, Harbin, 2011.
- Ü. Yüceer, Discrete convexity: convexity for functions defined on discrete spaces, Discrete Appl. Math. 119 (2002), no. 3, 297–304.
Language: English
Submitted on: Jan 12, 2025
Accepted on: Mar 10, 2026
Published on: Apr 4, 2026
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