The Journal of the Indian Mathematical Society

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New Bounds for the Jensen-Dragomir Functional with Applications in Analysis


Affiliations
1 Department of Mathematics, Sirjan University Of Technology, Sirjan, Iran, Islamic Republic of
2 Department of Mathematics, University of Jiroft, Jiroft, Iran, Islamic Republic of
     

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The normalised Jensen functional is an important functional in theory of inequalities and it has been a subject of study in its own right. In this paper, we establish new bounds for Jensen’s discrete inequality. Also, we improve the basic result of Dragomir through a stronger refinement of Jensens inequality which is then applied to analysis and information theory.


Keywords

Shannon’s Entropy, Jensen’s Inequality, Dragomir’s Inequality, Convex Function.
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  • 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 (1) (2001) Art. 5.

  • S. S. Dragomir, Bounds for the Normalised Jensen Functional, Bull. Austral. Math. Soc., 74 (2006), 471–478.

  • S. S. Dragomir, A converse result for Jensen’s discrete inequality via Grss inequality and applications in information theory, An. Univ. Oradea. Fasc. Mat. 7 (1999-2000), 178–189.

  • S. S. Dragomir, C. J. Goh, Some bounds on entropy measures in Information Theory, Appl. Math. Lett. 10 (3) (1997), 23–28.

  • JLWV Jensen, Om konvekse Funktioner og Uligheder mellem Middelvrdier, Nyt Tidsskr Math B, 16 (1905), 49–68 (in Danish).

  • A. McD. Mercer, A variant of Jensen’s inequality, J. Ineq. Pur. and Appl. Math., 4 (4) (2003), Article 73.

  • D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and new inequalities in analysis, Kluwer Academic Publishers, Dordrecht, 1993.

  • Y. Sayyari, An improvement of the upper bound on the entropy of information sources, J. Math. Ext., 15 (5) (2021), 1–12.

  • Y. Sayyari, New bounds for entropy of information sources, Wave. and Lin. Algeb., 7 (2) (2020), 1–9.

  • Y. Sayyari, New entropy bounds via uniformly convex functions, Chaos, Solitons and Fractals, 141 (1) (2020), (DOI: 10.1016/j.chaos.2020.110360).

  • Y. Sayyari, New refinements of Shannons entropy upper bounds, J. Inform. Optim. Sci., 42 (8) (2021), 1869–1883.

  • Y. Sayyari, A refinement of the Jensen-Simic-Mercer inequality with applications to entropy, J. Korean Soc. Math. Edu. Ser. B-Pure and Appl. Math., 29 (1) (2022), 51–57.

  • Y. Sayyari, An extension of Jensen-Mercer inequality with application to entropy, Honam Math. J., 44 (4) (2022), 513–520.

  • Y. Sayyari, Remarks on uniformly convexity with applications in A-G-H inequality and entropy, Int. J. Nonlin. Anal. Appl., 13 (2) (2022), 131–139.

  • Y. Sayyari, M. R. Molaei and A. Mehrpooya, Complexities of information sourecs, J. Appl. Stat., (2022), 1–17, (DOI 10.1080/02664763.2022.2101631).

  • S. Simic, On a global bound for Jensen’s inequality, J. Math. Anal. Appl. 343 (2008), 414–419, (DOI 10.1016/j.jmaa.2008.01.060).

  • S. Simic, Jensens inequality and new entropy bounds, Appl. Math. Lett. 22 (8) (2009), 1262–1265.


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  • New Bounds for the Jensen-Dragomir Functional with Applications in Analysis

Abstract Views: 180  |  PDF Views: 0

Authors

Yamin Sayyari
Department of Mathematics, Sirjan University Of Technology, Sirjan, Iran, Islamic Republic of
Mehdi Dehghanian
Department of Mathematics, Sirjan University Of Technology, Sirjan, Iran, Islamic Republic of
Hasan Barsam
Department of Mathematics, University of Jiroft, Jiroft, Iran, Islamic Republic of

Abstract


The normalised Jensen functional is an important functional in theory of inequalities and it has been a subject of study in its own right. In this paper, we establish new bounds for Jensen’s discrete inequality. Also, we improve the basic result of Dragomir through a stronger refinement of Jensens inequality which is then applied to analysis and information theory.


Keywords


Shannon’s Entropy, Jensen’s Inequality, Dragomir’s Inequality, Convex Function.

References