Remarks on uniformly convexity with applications in A-G-H inequality and entropy

Document Type : Research Paper


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


In this work, we shall give an upper bound for Jensen’s inequality (for uniformly convex functions). Also, we introduce a refinement for the generalized $A-G-H$ inequality. Applying those results in information theory and obtain bounds for entropy.


[1] I. Budimir, S.S. Dragomir, J. Pecaric, Further reverse results for Jensen’s discrete inequality and applications in
information theory, J. Inequal. Pure Appl. Math. 2 (2001), no. 1, Art. 5.
[2] H. H. Bauschke and P. L. Combettes, Convex analysis and monotone operator theory in Hilbert Spaces, SpringerVerlag, 2011.
[3] Ch. Corda, M. FatehiNia, M.R. Molaei and Y. Sayyari, Entropy of iterated function systems and their relations
with black holes and Bohr-like black holes entropies, Entropy 20 (2018), no. 1, 56.
[4] S.S. Dragomir, A converse result for Jensen’s discrete inequality via Gr¨uss inequality and applications in information theory, An. Univ. Oradea. Fasc. Mat. 7 (1999-2000), 178–189.
[5] M. Eshaghi Gordji, S.S. Dragomir and M. Rostamian Delavara, An inequality related to η-convex functions (II),
Int. J. Nonlinear Anal. Appl. 6 (2015), no. 2, 27–33
[6] A. Mehrpooya, Y. Sayyari and M.R. Molaei, Algebraic and Shannon entropies of commutative hypergroups and
their connection with information and permutation entropies and with calculation of entropy for chemical algebras,
Soft Comput. 23 (2019), no. 24, 13035–13053.
[7] D.S. Mitrinovic, Analytic inequalities, Springer, New York, 1970.
[8] Y. Sayyari, A refinement of the Jensen-Simic-Mercer inequality with applications to entropy, Pure Appl. Math.
29 (2022), no. 1, 51–57.
[9] Y Sayyari, New refinements of Shannon’s entropy upper bounds,, J. Inf. Optim. Sci. 42 (2021), no. 8, 1869–1883.
[10] Y. Sayyari, An improvement of the upper bound on the entropy of information sources, J. Math. Ext. 15 (2021),
no. 2, 1–12.
[11] Y. Sayyari, New entropy bounds via uniformly convex functions, Chaos Solitons Fractals 141 (2020), no. 1, 110360.
[12] Y. Sayyari, New bounds for entropy of information sources, Wavelets Linear Algebra 7 (2020), no. 2, 1–9.
[13] S. Simic, On a global bound for Jensen’s inequality, J. Math. Anal. Appl. 343 (2008), 414–419.
[14] S. Simic, Jensen’s inequality and new entropy bounds, Appl. Math. Lett. 22 (2009), no. 8, 1262–1-265.
[15] S. Simic, Sharp global bounds for Jensen’s inequality, Rock. Mount. J. Math. 41 (2011), no. 6, 2021–2031.
Volume 13, Issue 2
July 2022
Pages 131-139
  • Receive Date: 03 August 2021
  • Revise Date: 29 August 2021
  • Accept Date: 07 May 2022