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On logarithmic convexity for differences of power means. (English) Zbl 1133.26007

Summary: We prove a new and precise inequality between the differences of power means. As a consequence, an improvement of Jensen’s inequality and a converse of Hölder’s inequality are obtained. Some applications in probability and information theory are also given.

MSC:

26A51 Convexity of real functions in one variable, generalizations
26E60 Means
26D15 Inequalities for sums, series and integrals
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References:

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