On the speed of convergence of iteration of a function
Let fn(x) be the nth iterate of a function in some interval [0,c]. It is known that if f(x)∼x−xα, α>1, then fn(x)∼Ana for some A and a. In this paper we prove a converse of this theorem: The rate of convergence of the iterates determines the form of a function.
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000050 |
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| _version_ | 1849471790006403072 |
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| author | Vladimir Drobot |
| author_facet | Vladimir Drobot |
| author_sort | Vladimir Drobot |
| collection | DOAJ |
| description | Let fn(x) be the nth iterate of a function in some interval [0,c]. It is known that if f(x)∼x−xα, α>1, then fn(x)∼Ana for some A and a. In this paper we prove a converse of this theorem: The rate of convergence of the iterates determines the form of a function. |
| format | Article |
| id | doaj-art-e7185e9aa0de4152a6c3eade8664fa88 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e7185e9aa0de4152a6c3eade8664fa882025-08-20T03:24:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-01171313610.1155/S0161171294000050On the speed of convergence of iteration of a functionVladimir Drobot0Department of Mathematics and Computer Science, San Jose State University, San Jose 95192, CA, USALet fn(x) be the nth iterate of a function in some interval [0,c]. It is known that if f(x)∼x−xα, α>1, then fn(x)∼Ana for some A and a. In this paper we prove a converse of this theorem: The rate of convergence of the iterates determines the form of a function.http://dx.doi.org/10.1155/S0161171294000050iterations of a functionslow convergence. |
| spellingShingle | Vladimir Drobot On the speed of convergence of iteration of a function International Journal of Mathematics and Mathematical Sciences iterations of a function slow convergence. |
| title | On the speed of convergence of iteration of a function |
| title_full | On the speed of convergence of iteration of a function |
| title_fullStr | On the speed of convergence of iteration of a function |
| title_full_unstemmed | On the speed of convergence of iteration of a function |
| title_short | On the speed of convergence of iteration of a function |
| title_sort | on the speed of convergence of iteration of a function |
| topic | iterations of a function slow convergence. |
| url | http://dx.doi.org/10.1155/S0161171294000050 |
| work_keys_str_mv | AT vladimirdrobot onthespeedofconvergenceofiterationofafunction |