科研之友
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摘要
The iterative k- variable means, i. e. the means of the form M (x1,..., xk) = (k i= 1 ai f i xi) where f maps a real interval I into itself, f i is the ith iterate of f, and a1,..., ak are real numbers, are considered. Reflexivity of such a mean reduces to a polynomial type iterative functional equation. The conditions under which Mf is a mean and a strict mean are given. In the case k = 2 the invariance of the quasi- arithmetic mean with respect to the iterativemean- type mappings are considered and, as an application, some functional equations are effectively solved. Possible generalizations are mentioned.
- 出版日期2018
- 单位西南交通大学
