Abstract
The power means are defined using the convex, or concave, power, logarithmic and exponential functions. In this chapter means are defined using arbitrary convex and concave functions by a natural extension of the classical definitions and analogues of the basic results of the earlier chapters are investigated. First however we take up the problem of different convex functions defining the same means; the case of equivalent means. The generalizations (GA) and (r;s), their converses and the Rado-Popoviciu type extensions are studied under the topic of comparable means. The definition can be further extended although this leads to the topics of functional equations and functional inequalities so is not followed in detail.
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). Quasi-Arithmetic 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_4
Download citation
DOI: https://doi.org/10.1007/978-94-017-0399-4_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6383-0
Online ISBN: 978-94-017-0399-4
eBook Packages: Springer Book Archive