Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application
In this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2×2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. These results are formulated in terms of weak sequential continuity and...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9985817 |
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| _version_ | 1832546040424693760 |
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| author | Mohamed Amine Farid El Miloudi Marhrani Mohamed Aamri |
| author_facet | Mohamed Amine Farid El Miloudi Marhrani Mohamed Aamri |
| author_sort | Mohamed Amine Farid |
| collection | DOAJ |
| description | In this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2×2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. These results are formulated in terms of weak sequential continuity and the technique of De Blasi measure of weak noncompactness on countably subsets. We will also prove the existence of solutions for a coupled system of nonlinear equations with an example. |
| format | Article |
| id | doaj-art-15f0d4d1325f4afba17a214fb1fb8369 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-15f0d4d1325f4afba17a214fb1fb83692025-02-03T07:23:54ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99858179985817Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an ApplicationMohamed Amine Farid0El Miloudi Marhrani1Mohamed Aamri2L3A Laboratory, Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’sik, University of Hassan II, Casablanca, MoroccoL3A Laboratory, Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’sik, University of Hassan II, Casablanca, MoroccoL3A Laboratory, Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’sik, University of Hassan II, Casablanca, MoroccoIn this paper, we establish some new variants of Leray–Schauder-type fixed point theorems for a 2×2 block operator matrix defined on nonempty, closed, and convex subsets Ω of Banach spaces. Note here that Ω need not be bounded. These results are formulated in terms of weak sequential continuity and the technique of De Blasi measure of weak noncompactness on countably subsets. We will also prove the existence of solutions for a coupled system of nonlinear equations with an example.http://dx.doi.org/10.1155/2021/9985817 |
| spellingShingle | Mohamed Amine Farid El Miloudi Marhrani Mohamed Aamri Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application Journal of Mathematics |
| title | Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application |
| title_full | Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application |
| title_fullStr | Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application |
| title_full_unstemmed | Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application |
| title_short | Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application |
| title_sort | leray schauder fixed point theorems for block operator matrix with an application |
| url | http://dx.doi.org/10.1155/2021/9985817 |
| work_keys_str_mv | AT mohamedaminefarid lerayschauderfixedpointtheoremsforblockoperatormatrixwithanapplication AT elmiloudimarhrani lerayschauderfixedpointtheoremsforblockoperatormatrixwithanapplication AT mohamedaamri lerayschauderfixedpointtheoremsforblockoperatormatrixwithanapplication |