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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.

26D15Inequalities for sums, series and integrals of real functions
52A40Inequalities and extremum problems (convex geometry)
Full Text: DOI
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