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.


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