Abstract
This chapter is devoted to the properties and inequalities of the classical arithmetic, geometric and harmonic means. In particular the basic inequality between these means, the Geometric Mean-Arithmetic Mean Inequality, is discussed at length with many proofs being given. Various refinements of this basis inequality are then considered; in particular the Rado-Popoviciu type inequalities and the Nanjundiah inequalities. Converse inequalities are discussed as well as Čebišev’s inequality. Some simple properties of the logarithmic and identric means are obtained.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bullen, P.S. (2003). The Arithmetic, Geometric and Harmonic 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_2
Download citation
DOI: https://doi.org/10.1007/978-94-017-0399-4_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6383-0
Online ISBN: 978-94-017-0399-4
eBook Packages: Springer Book Archive