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Reverses of the Jensen-Type Inequalities for Signed Measures

Author

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  • Rozarija Jakšić
  • Josip Pečarić
  • Mirna Rodić Lipanović

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.

Suggested Citation

  • Rozarija Jakšić & Josip Pečarić & Mirna Rodić Lipanović, 2014. "Reverses of the Jensen-Type Inequalities for Signed Measures," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, August.
    • Handle: RePEc:hin:jnlaaa:626359
    DOI: 10.1155/2014/626359
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