Generalization of the Levinson inequality with applications to information theory View Full Text


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Article Info

DATE

2019-08-29

AUTHORS

Muhammad Adeel, Khuram Ali Khan, Ðilda Pečarić, Josip Pečarić

ABSTRACT

In the presented paper, Levinson’s inequality for the 3-convex function is generalized by using two Green functions. Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, the main results are applied to information theory via the f-divergence, the Rényi divergence, the Rényi entropy, the Shannon entropy and the Zipf–Mandelbrot law. More... »

PAGES

230

References to SciGraph publications

  • 2015-07-28. Superadditivity of the Levinson functional and applications in PERIODICA MATHEMATICA HUNGARICA
  • 2018-02-08. Zipf–Mandelbrot law, f-divergences and the Jensen-type interpolating inequalities in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2017-07-28. Estimations of f- and Rényi Divergences by Using a Cyclic Refinement of the Jensen’s Inequality in BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • 2018-11-19. Refinement of Jensen’s inequality and estimation of f- and Rényi divergence via Montgomery identity in JOURNAL OF INEQUALITIES AND APPLICATIONS
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    http://scigraph.springernature.com/pub.10.1186/s13660-019-2186-4

    DOI

    http://dx.doi.org/10.1186/s13660-019-2186-4

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