Iterative functional equations and means. Issue 5 (4th May 2018) - Liu, Liu; Matkowski, Janusz
Abstract : The iterative k -variable means, i.e. the means of the formM x 1, …, x k = ∑ i = 1 k a i f i x i where f maps a real interval I into itself, f i is the i th iterate of f, anda 1, …, a k are real numbers, are considered. Reflexivity of such a mean reduces to a polynomial type iterative functional equation. The conditions under whichM f is a mean and a strict mean are given. In the casek = 2 the invariance of the quasi-arithmetic mean with respect to the iterative mean-type mappings are considered and, as an application, some functional equations are effectively solved. Possible generalizations are mentioned.