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Eine Integralungleichung für streng monotone Funktionen mit logarithmisch konvexer Umkehrfunktion. (An integral inequality for strictly monotonic functions with a logarithmically convex inverse function). (German) Zbl 0721.26010
The author proves the following result: If f is a strictly increasing [resp. decreasing] continuous function on $$[a,b],\quad 0<a<b,$$ having a logarithmically convex inverse function, then $(1)\quad (b-a)^{- 1}\int^{b}_{a}f(x)dx\leq [resp.\quad \geq]f(I(a,b)),$ where I(a,b) (the so-called “identric-mean”) is defined by $$I(a,b)=e^{-1}\cdot (b^ b/a^ a)^{1/(b-a)}$$ for $$a\neq b$$, $$I(a,a)=a$$. He also gives an interesting application for K. B. Stolarsky’s means [Math. Mag. 48, 87-92 (1975; Zbl 0302.26003)].

##### MSC:
 26D15 Inequalities for sums, series and integrals
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