Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability
This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/948749 |
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| _version_ | 1832558752728875008 |
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| author | Manuel De la Sen Asier Ibeas |
| author_facet | Manuel De la Sen Asier Ibeas |
| author_sort | Manuel De la Sen |
| collection | DOAJ |
| description | This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems. |
| format | Article |
| id | doaj-art-c04280be82a8415e91480ef39155a8a5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c04280be82a8415e91480ef39155a8a52025-02-03T01:31:41ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/948749948749Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global StabilityManuel De la Sen0Asier Ibeas1Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644, Barrio Sarriena, 48940 Leioa, SpainDepartment of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona (UAB), 08193 Barcelona, SpainThis paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.http://dx.doi.org/10.1155/2014/948749 |
| spellingShingle | Manuel De la Sen Asier Ibeas Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability Abstract and Applied Analysis |
| title | Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability |
| title_full | Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability |
| title_fullStr | Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability |
| title_full_unstemmed | Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability |
| title_short | Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability |
| title_sort | convergence properties and fixed points of two general iterative schemes with composed maps in banach spaces with applications to guaranteed global stability |
| url | http://dx.doi.org/10.1155/2014/948749 |
| work_keys_str_mv | AT manueldelasen convergencepropertiesandfixedpointsoftwogeneraliterativeschemeswithcomposedmapsinbanachspaceswithapplicationstoguaranteedglobalstability AT asieribeas convergencepropertiesandfixedpointsoftwogeneraliterativeschemeswithcomposedmapsinbanachspaceswithapplicationstoguaranteedglobalstability |