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Licensed Unlicensed Requires Authentication Published by Oldenbourg Wissenschaftsverlag February 2, 2016

Cyclic refinements of the discrete and integral form of Jensen’s inequality with applications

László Horváth , Khuram Ali Khan EMAIL logo and Josip Pečarić
From the journal Analysis


In this paper we introduce new refinements of both the discrete and the classical Jensen’s inequality. First, we give the weighted version of a recent cyclic refinement. By using this result, we obtain new refinements of the classical Jensen’s inequality. We investigate m-exponential convexity of some functionals coming from the new refinements. To apply our results we define some new mixed symmetric means, generalized means, and Cauchy means, and study their properties.

MSC 2010: 26A51; 26D15; 26E60

Funding statement: The research of the third author was partially supported by the Croatian Science Foundation under project 5435.


[1] Brnetić I., Khan K. A. and Pečarić J., Refinement of Jensen’s inequality with applications to cyclic mixed symmetric means and Cauchy means, J. Math. Inequal. 9 (2015), no. 4, 1309–1321. 10.7153/jmi-09-100Search in Google Scholar

[2] Horváth L., Inequalities corresponding to the classical Jensen’s inequality, J. Math. Inequal. 3 (2009), no. 2, 189–200. 10.7153/jmi-03-19Search in Google Scholar

[3] Horváth L., Khan K. A. and Pečarić J., Combinatorial Improvements of Jensen’s Inequality, Monogr. Inequal. 8, Element, Zagreb, 2014. Search in Google Scholar

[4] Pečarić J. and Perić J., Improvement of the Giaccardi and the Petrović inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform. 39 (2012), no. 1, 65–75. Search in Google Scholar

Received: 2015-5-18
Revised: 2015-11-18
Accepted: 2016-1-20
Published Online: 2016-2-2
Published in Print: 2016-11-1

© 2016 by De Gruyter

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