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Jessen’s functional, its properties and applications. (English) Zbl 1274.26058
Summary: We consider Jessen’s functional, defined by means of a positive isotonic linear functional, and investigate its properties. Derived results are then applied to weighted generalized power means, which yields extensions of some recent results, known from the literature. In particular, we obtain a whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young’s inequality and Hölders inequality.

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