Abstract
This chapter is devoted to the properties and inequalities of the classical generalization of the arithmetic, geometric and harmonic means, the power means. The inequalities obtained in the previous chapter are extended to this scale of means. In addition some results for sums of powers are obtained, the classical inequalities of Minkowski, Cauchy and Hölder, and some generalization of these results. Various generalizations of the power mean family are also discussed.
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© 2003 Springer Science+Business Media Dordrecht
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Bullen, P.S. (2003). The Power Means. In: Handbook of Means and Their Inequalities. Mathematics and Its Applications, vol 560. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0399-4_3
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DOI: https://doi.org/10.1007/978-94-017-0399-4_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6383-0
Online ISBN: 978-94-017-0399-4
eBook Packages: Springer Book Archive