Journal of Convex Analysis 31 (2024), No. 1, 279--287
Copyright Heldermann Verlag 2024
Refining the Superadditivity Inequality for Weighted Jensen and Mercer Functionals
Marek Niezgoda
Institute of Mathematics, Pedagogical University of Cracow, Cracow, Poland
bniezgoda@wp.pl
The Jensen and Mercer functionals viewed as functions of their weighted vectors are superadditive as showed by S. S. Dragomir, J. E. Pecaric 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. Krnic, N. Lovricevic and J. Pecaric [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.
Keywords: Convex function, Jensen inequality, Mercer inequality, superadditive function, preorder, DPP/KLP inequalities, positive homogeneous function, monotone functional.
MSC: 26D15, 26A51, 52A41.
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