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Inequalities for the normalized Jensen functional with applications

  • Hossein Dehghan EMAIL logo
Published/Copyright: April 26, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

In this paper we present some new inequalities for the normalized Jensen functional which will much improve the famous Jensen’s inequality. We also give some applications in Analysis and Information Theory. Our results refine and generalize the corresponding ones announced in [DRAGOMIR, S. S.: Bounds for the normalised Jensen functional, Bull. Aust. Math. Soc. 74 (2006), 471–478] and [MITANI, K. I. et al.: On sharp triangle inequalities in Banach spaces, J. Math. Anal. Appl. 336 (2007), 1178–1186].

Keywords: plant disease; Jensen’s inequality; convex function; triangle inequality
MSC: Primary 26D15; 26B25

  1. This paper has been communicated by Ján Borsík.

Acknowledgement

The author wishes to thank Professor J. Rooin for proposing Convexity to solve original problem.

References

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Received: 2012-6-20
Accepted: 2013-5-17
Published Online: 2016-4-26
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0121
Keywords for this article
plant disease; Jensen’s inequality; convex function; triangle inequality

Articles in the same Issue

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  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
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  9. Research Article
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  11. Research Article
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  13. Research Article
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  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
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