Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9492821 | Expositiones Mathematicae | 2005 | 24 Pages |
Abstract
In part 1, given n different ways of averaging n positive numbers, we iterate the resulting map in (0,â)n. We prove convergence toward the diagonal, with rate estimates under smoothness assumptions. In part 2, we consider the elementary symmetric means of order p applied to the values ai=a(i/n),1⩽i⩽n, of a given continuous positive function a on the normalized interval [0,1] and we let p=f(n). When limnââf(n)/n=0, we prove that it admits a limit as nââ, called the f-mean of a, which moreover coincides with â«01a(x)dx whenever f(n)=o(logn). We record similar, quite immediate, results on the geometric side p=n-f(n).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Philippe Delanoë,