Properties of some functionals related to Jensen’s inequality. (English) Zbl 0847.26013

Dragomir, Sever Silvestru; Pečarić, Josip E.; Persson, L. E.

Acta Math. Hung. 70, No. 1-2, 129-143 (1996).

The authors offer generalizations of the weighted Jensen inequality (which is the definition of convex functions) to real linear spaces. They explore their connections to superadditivity, supermultiplicativity and sublinearity, and apply the results to similar generalizations of the Hölder, Minkowski, arithmetic and geometric mean etc. inequalities.
In the last line of p. 129 “positive” (nonnegative?) is missing before “for all”.

Reviewer: J.Aczél (Waterloo / Ontario)

MSC:

26D15	Inequalities for sums, series and integrals
26A51	Convexity of real functions in one variable, generalizations
39B72	Systems of functional equations and inequalities

Keywords:

Hölder inequality; Minkowski inequality; arithmetic and geometric mean inequality; weighted Jensen inequality; superadditivity; supermultiplicativity; sublinearity

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