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

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.