Abstract

The Jensen and Mercer functionals viewed as functions of their weighted vectors are superadditive as showed by S. S. Dragomir, J. E. Pečarić and L. E. Persson [Properties of some functionals related to Jensen's inequality, Acta Math. Hung. 70/1-2 (1996) 129–143] and by M. Krnić, N. Lovričević and J. Pečarić [On some properties of Jensen-Mercer's functional, J. Math. Inequalities 6/1 (2012) 125–139]. In the present paper we derive refinements of the corresponding superadditivity DPP/KLP inequalities. We establish Jensen and Mercer inequalities of second type. We introduce a preorder on the set of weighted vectors and show the monotonicity with respect to this preorder of a functional related to Jensen/Mercer inequality.

Author information

Contact details are reproduced from the original publication and may be historical.

Marek Niezgoda

Institute of Mathematics, Pedagogical University of Cracow, Cracow, Poland

bniezgoda@wp.pl

Keywords

  • Convex function
  • Jensen inequality
  • Mercer inequality
  • superadditive function
  • preorder
  • DPP/KLP inequalities
  • positive homogeneous function
  • monotone functional

Mathematics Subject Classification

26D15, 26A51, 52A41

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Suggested citation

M. Niezgoda. “Refining the Superadditivity Inequality for Weighted Jensen and Mercer Functionals.” Journal of Convex Analysis 31 (2024), No. 1, 279–287. https://doi.org/10.68381/jca31017

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.