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

László Horváth 1 , Khuram Ali Khan 2 ,  and Josip Pečarić 3
  • 1 Department of Mathematics, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary
  • 2 Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
  • 3 Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
László Horváth, Khuram Ali Khan and Josip Pečarić

Abstract

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.

  • [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.

  • [2]

    Horváth L., Inequalities corresponding to the classical Jensen’s inequality, J. Math. Inequal. 3 (2009), no. 2, 189–200.

  • [3]

    Horváth L., Khan K. A. and Pečarić J., Combinatorial Improvements of Jensen’s Inequality, Monogr. Inequal. 8, Element, Zagreb, 2014.

  • [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.

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Analysis is devoted to the field of mathematical analysis, in particular classical analysis and its applications. Its aim is to publish the best research articles within the scope of the journal, as well as to boost the cooperation between scholars.

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