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

Toader, Gh.

Stud. Univ. Babeș-Bolyai, Math. 39, No. 2, 27-32 (1994).

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.

Reviewer: I.Raşa (Cluj-Napoca)

MSC:

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

Keywords:

Hermite-Hadamard inequalities; superadditivity; convex functions