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

László Horváth, Khuram Ali Khan 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.


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

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