A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces
Inspired by the modified iteration method devised by He and Zhu [1], the purpose of this paper is to present a modified Krasnoselskii iteration via boundary method. A strong convergence theorem of this iteration for finding minimum norm solution of nonlinear equation of the form Sh(x)(x)=0, where Sh...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2014-10-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X13001533 |
| _version_ | 1818261214849925120 |
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| author | A.M. Saddeek |
| author_facet | A.M. Saddeek |
| author_sort | A.M. Saddeek |
| collection | DOAJ |
| description | Inspired by the modified iteration method devised by He and Zhu [1], the purpose of this paper is to present a modified Krasnoselskii iteration via boundary method. A strong convergence theorem of this iteration for finding minimum norm solution of nonlinear equation of the form Sh(x)(x)=0, where Sh(x) is a nonlinear mapping of C into itself and h is a function of C into [0,1] is then proved in Hilbert spaces. In the same vein, an application to the stationary problem of seepage theory is also presented. The results of this paper are extensions and improvements of some earlier theorems of Saddeek et al. [2]. |
| first_indexed | 2024-12-12T18:43:41Z |
| format | Article |
| id | doaj.art-f2fe866f984a4fdfa0f62c5f18e88cc4 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-12T18:43:41Z |
| publishDate | 2014-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-f2fe866f984a4fdfa0f62c5f18e88cc42022-12-22T00:15:35ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2014-10-0122347648010.1016/j.joems.2013.12.012A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spacesA.M. SaddeekInspired by the modified iteration method devised by He and Zhu [1], the purpose of this paper is to present a modified Krasnoselskii iteration via boundary method. A strong convergence theorem of this iteration for finding minimum norm solution of nonlinear equation of the form Sh(x)(x)=0, where Sh(x) is a nonlinear mapping of C into itself and h is a function of C into [0,1] is then proved in Hilbert spaces. In the same vein, an application to the stationary problem of seepage theory is also presented. The results of this paper are extensions and improvements of some earlier theorems of Saddeek et al. [2].http://www.sciencedirect.com/science/article/pii/S1110256X13001533Krasnoselskii iterationStrong convergenceMinimum norm solutionPseudomonotone mappingsLipschitzian mappingsSeepage theory |
| spellingShingle | A.M. Saddeek A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces Journal of the Egyptian Mathematical Society Krasnoselskii iteration Strong convergence Minimum norm solution Pseudomonotone mappings Lipschitzian mappings Seepage theory |
| title | A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces |
| title_full | A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces |
| title_fullStr | A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces |
| title_full_unstemmed | A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces |
| title_short | A strong convergence theorem for a modified Krasnoselskii iteration method and its application to seepage theory in Hilbert spaces |
| title_sort | strong convergence theorem for a modified krasnoselskii iteration method and its application to seepage theory in hilbert spaces |
| topic | Krasnoselskii iteration Strong convergence Minimum norm solution Pseudomonotone mappings Lipschitzian mappings Seepage theory |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X13001533 |
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