Invariance in some families of means. (English) Zbl 1251.26019
Rassias, Themistocles M. (ed.) et al., Functional equations in mathematical analysis. Dedicated to the memory of Stanisław Marcin Ulam on the occasion of the 100th anniversary of his birth. Berlin: Springer (ISBN 978-1-4614-0054-7/hbk; 978-1-4614-0055-4/ebook). Springer Optimization and Its Applications 52, 709-717 (2011).
Summary: A mean \(P\) is \((M,N)\)-invariant if \(P(M,N) = P\). In the same time the mean \(N\) is called complementary to \(M\) with respect to \(P\). For the determination of complementaries, three methods have been used: the direct calculation, the methods of functional equations, and the series expansion of means. In the current paper we consider the method of series expansion of means to study the invariance in the family of extended logarithmic means.
For the entire collection see [Zbl 1225.39001].
For the entire collection see [Zbl 1225.39001].
MSC:
| 26E60 | Means |
