Invariance in the class of weighted quasi-arithmetic means
Volume 88 / 2006
Annales Polonici Mathematici 88 (2006), 39-51
MSC: Primary 26E60; Secondary 39B22.
DOI: 10.4064/ap88-1-3
Abstract
Under the assumption of twice continuous differentiability of some of the functions involved we determine all the weighted quasi-arithmetic means $M,N,K$ such that $K$ is $(M,N)$-invariant, that is, $K\circ (M,N)=K.$ Some applications to iteration theory and functional equations are presented.
