The approximation of the solutions of equations using approximant sequences
We intend to characterize the convergence of a certain sequence that belongs to a subset of a Banach space towards the solution of an equation obtained by the annulment of a nonlinear mapping that is defined on this subset and that takes values in another linear normed space. This mapping ha...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
2003-02-01
|
| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/731 |
| _version_ | 1811291505465229312 |
|---|---|
| author | Adrian Diaconu |
| author_facet | Adrian Diaconu |
| author_sort | Adrian Diaconu |
| collection | DOAJ |
| description | We intend to characterize the convergence of a certain sequence
that belongs to a subset of a Banach space towards the solution of
an equation obtained by the annulment of a nonlinear mapping that
is defined on this subset and that takes values in another linear
normed space. This mapping has a Fréchet derivative of a
certain order which verifies the Lipschitz condition. We can
establish some conditions that are enough both for the existence
of the equation's solution and for a speed of convergence of a
certain order for the approximant sequence. |
| first_indexed | 2024-04-13T04:30:27Z |
| format | Article |
| id | doaj.art-6ab8a9b419a34f3bb11aff41947a38bc |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-13T04:30:27Z |
| publishDate | 2003-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-6ab8a9b419a34f3bb11aff41947a38bc2022-12-22T03:02:21ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2003-02-01321The approximation of the solutions of equations using approximant sequencesAdrian Diaconu0“Babes-Bolyai” University, Cluj-Napoca, RomaniaWe intend to characterize the convergence of a certain sequence that belongs to a subset of a Banach space towards the solution of an equation obtained by the annulment of a nonlinear mapping that is defined on this subset and that takes values in another linear normed space. This mapping has a Fréchet derivative of a certain order which verifies the Lipschitz condition. We can establish some conditions that are enough both for the existence of the equation's solution and for a speed of convergence of a certain order for the approximant sequence.https://ictp.acad.ro/jnaat/journal/article/view/731convergence of the approximant sequences for operatorial equations in Banach spaces |
| spellingShingle | Adrian Diaconu The approximation of the solutions of equations using approximant sequences Journal of Numerical Analysis and Approximation Theory convergence of the approximant sequences for operatorial equations in Banach spaces |
| title | The approximation of the solutions of equations using approximant sequences |
| title_full | The approximation of the solutions of equations using approximant sequences |
| title_fullStr | The approximation of the solutions of equations using approximant sequences |
| title_full_unstemmed | The approximation of the solutions of equations using approximant sequences |
| title_short | The approximation of the solutions of equations using approximant sequences |
| title_sort | approximation of the solutions of equations using approximant sequences |
| topic | convergence of the approximant sequences for operatorial equations in Banach spaces |
| url | https://ictp.acad.ro/jnaat/journal/article/view/731 |
| work_keys_str_mv | AT adriandiaconu theapproximationofthesolutionsofequationsusingapproximantsequences AT adriandiaconu approximationofthesolutionsofequationsusingapproximantsequences |