International Journal of Nonlinear Analysis and Applications

On cubic convex functions and applications in information theory

Document Type : Research Paper

Authors

Department of Mathematics, Sirjan University of Technology, Sirjan, Iran

Abstract

‎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.

Keywords

[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.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 10
October 2023
Pages 77-83
  • Receive Date: 02 November 2022
  • Revise Date: 06 February 2023
  • Accept Date: 11 February 2023