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

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