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Refinements of Jessen’s functional. (English) Zbl 1499.26093

Ukr. Math. J. 68, No. 7, 1000-1020 (2016) and Ukr. Mat. Zh. 68, No. 7, 879-896 (2016).
Summary: We obtain new refinements of Jessen’s functional defined by means of positive linear functionals. The accumulated results are applied to weighted generalized and power means. We also obtain new refinements of numerous classical inequalities, such as the arithmetic-geometric mean inequality, Young’s inequality, and Hölder’s inequality.

MSC:

26D15 Inequalities for sums, series and integrals
26E60 Means
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References:

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