Some Results on Fixed Point Theorems in Banach Algebras
<p>Let X be a Banach algebra and D be a nonempty subset of X. Let (T 1, T 2) be a pair of self mappings on D satisfying some specific conditions. Here we discuss different situations for existence of solution of the operator equation u = T 1 uT 2 u in D. Similar results are established in case...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2017-01-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://www.etamaths.com/index.php/ijaa/article/view/839 |
| _version_ | 1819116676674748416 |
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| author | Dipankar Das Nilakshi Goswami Vishnu Narayan Mishra |
| author_facet | Dipankar Das Nilakshi Goswami Vishnu Narayan Mishra |
| author_sort | Dipankar Das |
| collection | DOAJ |
| description | <p>Let X be a Banach algebra and D be a nonempty subset of X. Let (T 1, T 2) be a pair of self mappings on D satisfying some specific conditions. Here we discuss different situations for existence of solution of the operator equation u = T 1 uT 2 u in D. Similar results are established in case of reflexive Banach algebra X with the subset D. Again, considering a bounded, open and convex subset B in a uniformly convex Banach algebra X with three self mappings T 1 ,T 2 ,T 3 on B, we derive the conditions for existence of solution of the operator equation u = T 1 uT 2 u + T 3 u in B. Application of some of these results to the tensor product is also shown here with some examples.</p> |
| first_indexed | 2024-12-22T05:20:53Z |
| format | Article |
| id | doaj.art-c7e3dbedb2bc4069bcc35eafec8c1bc6 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-22T05:20:53Z |
| publishDate | 2017-01-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-c7e3dbedb2bc4069bcc35eafec8c1bc62022-12-21T18:37:43ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392017-01-011313240212Some Results on Fixed Point Theorems in Banach AlgebrasDipankar DasNilakshi GoswamiVishnu Narayan Mishra<p>Let X be a Banach algebra and D be a nonempty subset of X. Let (T 1, T 2) be a pair of self mappings on D satisfying some specific conditions. Here we discuss different situations for existence of solution of the operator equation u = T 1 uT 2 u in D. Similar results are established in case of reflexive Banach algebra X with the subset D. Again, considering a bounded, open and convex subset B in a uniformly convex Banach algebra X with three self mappings T 1 ,T 2 ,T 3 on B, we derive the conditions for existence of solution of the operator equation u = T 1 uT 2 u + T 3 u in B. Application of some of these results to the tensor product is also shown here with some examples.</p>http://www.etamaths.com/index.php/ijaa/article/view/839 |
| spellingShingle | Dipankar Das Nilakshi Goswami Vishnu Narayan Mishra Some Results on Fixed Point Theorems in Banach Algebras International Journal of Analysis and Applications |
| title | Some Results on Fixed Point Theorems in Banach Algebras |
| title_full | Some Results on Fixed Point Theorems in Banach Algebras |
| title_fullStr | Some Results on Fixed Point Theorems in Banach Algebras |
| title_full_unstemmed | Some Results on Fixed Point Theorems in Banach Algebras |
| title_short | Some Results on Fixed Point Theorems in Banach Algebras |
| title_sort | some results on fixed point theorems in banach algebras |
| url | http://www.etamaths.com/index.php/ijaa/article/view/839 |
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