Iterative functional equations and means. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Liu, Liu; Matkowski, Janusz
• Is Part Of: Journal of difference equations and applications. Volume 24:Issue 5(2018)
• Page Start: 797
• Page End: 811
• Publication Date: 2018-05-04
• Subjects: Mean -- reflexivity -- iterations -- composite functional equations -- invariant mean; Primary: 26A18 -- 26E60 -- 39B12; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2017.1356294
• Languages: English
• ISSNs: 1023-6198

Abstract

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.