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Superadditivity and Hermite-Hadamard’s inequalities. (English) Zbl 0868.26012

The author proves that the inequalities \[ f((a+ b)/2)\leq\Biggl(\int^b_a f(x)dx\Biggr)/(b-a)\leq (f(a)+ f(b))/2, \] well known for convex functions, hold in fact for some larger classes of functions and for functionals more general than integrals.

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
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