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Sharpening Hölder’s and Popoviciu’s inequalities via functionals. (English) Zbl 1119.26022

Summary: We prove some inequalities involving positive isotonic linear functionals which generalize Hölder’s inequality and its reverse version. We also sharpen Jensen’s inequalities for positive isotonic linear functionals.

MSC:

26D15 Inequalities for sums, series and integrals
52A40 Inequalities and extremum problems involving convexity in convex geometry
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