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A class of symmetric functions for multiplicatively convex function. (English) Zbl 1144.26015
Let \(f\) be a non-negative function defined on the positive semiaxis. The author associates to \(f\) a new symmetric function and the corresponding symmetric mean. Their properties, including Schur-geometric convexity, are investigated under the hypothesis that \(f\) is multiplicatively convex. Some inequalities are established, generalizing known results.

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