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On cubic convex functions and applications in information theory | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 8، دوره 14، شماره 10، دی 2023، صفحه 77-83 اصل مقاله (343.73 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28880.4010 | ||
| نویسندگان | ||
| Mehdi Dehghanian* ؛ Yamin Sayyari | ||
| Department of Mathematics, Sirjan University of Technology, Sirjan, Iran | ||
| تاریخ دریافت: 11 آبان 1401، تاریخ بازنگری: 17 بهمن 1401، تاریخ پذیرش: 22 بهمن 1401 | ||
| چکیده | ||
| In this paper, we introduce the cubic convex function and investigate Jensen type inequality, Fejér-Hermite-Hadamard type inequality and Mercer type inequality for cubic convex functions. Also, we give some applications in means and information theory by applying those inequalities. | ||
| کلیدواژه‌ها | ||
| cubic convex function؛ entropy؛ Fejér-Hermite-Hadamard inequality؛ Jensens inequality؛ Mercer inequality | ||
| مراجع | ||
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[1] S.S. Dragomir and C.J. Goh, Some bounds on entropy measures in information theory, Appl. Math. Lett. 10 (1997), no. 3, 23–28. [2] L. Fejer, Uberdie Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad. Wiss. 24 (1906), 369–390, (in Hungarian). [3] J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann, J. Math. Pures Appl. 58 (1893), 171–172. [4] J.L.W.V. Jensen, Om konvekse funktioner og uligheder mellem middelvaerdier, Nyt. Tidsskr. Math. B. 16 (1905), 49–68. [5] A.M. Mercer, A variant of Jensen’s inequality, J. Inequal. Pure Appl. Math. 4 (2003), no. 4. [6] Y. Sayyari, New entropy bounds via uniformly convex functions, Chaos, Solit. Fract. 141 (2020), 110360. [7] Y. Sayyari, A refinement of the Jensen-Simic-Mercer inequality with applications to entropy, Pure Appl. Math. 29 (2022), no. 1, 51–57. [8] Y. Sayyari, New refinements of Shannon’s entropy upper bounds, J. Inf. Optim. Sci. 42 (2021), no. 8, 1869–1883. [9] Y. Sayyari, An improvement of the upper bound on the entropy of information sources, J. Math. Ext. 15 (2021), no. 2, 1–12. [10] Y. Sayyari, Remarks on uniformly convexity with applications in A-G-H inequality and entropy, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 131–139. [11] Y. Sayyari, An extension of Jensen-mercer inequality with applications to entropy, Honam Math. J. 44 (2022), no. 4, 513–520. [12] Y. Sayyari, New bounds for entropy of information sources, Wavel. Lin. Algeb. 5 (2020), no. 3, 23–31. [13] Y. Sayyari, M. Dehghanian, C. Park and S. Paokanta, An extension of the Hermite-Hadamard inequality for a power of a convex function, Open Math. 21 (2023), no. 1, 1–11. [14] S. Simic, Jensen’s inequality and new entropy bounds, Appl. Math. Lett. 22 (2009), no. 8, 1262–1265. | ||
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