کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4640245 | 1341268 | 2011 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Continuity of iteration and approximation of iterative roots Continuity of iteration and approximation of iterative roots](/preview/png/4640245.png)
Motivated by computing iterative roots for general continuous functions, in this paper we prove the continuity of the iteration operators TnTn, defined by Tnf=fnTnf=fn. We apply the continuity and introduce the concept of continuity degree to answer positively the approximation question: If limm→∞Fm=Flimm→∞Fm=F, can we find an iterative root fmfm of FmFm of order nn for each m∈Nm∈N such that the sequence (fm)(fm) tends to the iterative root of FF of order nn associated with a given initial function? We not only give the construction of such an approximating sequence (fm)(fm) but also illustrate the approximation of iterative roots with an example. Some remarks are presented in order to compare our approximation with the Hyers–Ulam stability.
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 5, 1 January 2011, Pages 1232–1244