Reverses of the Jensen-Type Inequalities for Signed Measures

Rozarija Jakšić, Josip Pečarić and Mirna Rodić Lipanović

Abstract and Applied Analysis, 2014, vol. 2014, 1-11

Abstract:

In this paper we derive refinements of the Jensen type inequalities in the case of real Stieltjes measure , not necessarily positive, which are generalizations of Jensen's inequality and its reverses for positive measures. Furthermore, we investigate the exponential and logarithmic convexity of the difference between the left-hand and the right-hand side of these inequalities and give several examples of the families of functions for which the obtained results can be applied. The outcome is a new class of Cauchy-type means.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:626359

DOI: 10.1155/2014/626359

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