Perturbations of normally solvable nonlinear operators, I
Let X and Y be Banach spaces and let ℱ and 𝒢 be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+𝒢 is surjective for sufficiently small perturbations 𝒢 of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000266 |
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| _version_ | 1832551924335902720 |
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| author | William O. Ray Anita M. Walker |
| author_facet | William O. Ray Anita M. Walker |
| author_sort | William O. Ray |
| collection | DOAJ |
| description | Let X and Y be Banach spaces and let ℱ and 𝒢 be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+𝒢 is surjective for sufficiently small perturbations 𝒢 of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators. |
| format | Article |
| id | doaj-art-06398303a826467aa79d6efea540617b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-06398303a826467aa79d6efea540617b2025-02-03T05:59:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018224124610.1155/S0161171285000266Perturbations of normally solvable nonlinear operators, IWilliam O. Ray0Anita M. Walker1Department of Mathematics, The University of Oklahoma, Norman 73019, OK, USADepartment of Mathematics, The University of Oklahoma, Norman 73019, OK, USALet X and Y be Banach spaces and let ℱ and 𝒢 be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+𝒢 is surjective for sufficiently small perturbations 𝒢 of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.http://dx.doi.org/10.1155/S0161171285000266solvabilitynormal solvabitityinverse function theoremsEkeland's theoremcontractor directions. |
| spellingShingle | William O. Ray Anita M. Walker Perturbations of normally solvable nonlinear operators, I International Journal of Mathematics and Mathematical Sciences solvability normal solvabitity inverse function theorems Ekeland's theorem contractor directions. |
| title | Perturbations of normally solvable nonlinear operators, I |
| title_full | Perturbations of normally solvable nonlinear operators, I |
| title_fullStr | Perturbations of normally solvable nonlinear operators, I |
| title_full_unstemmed | Perturbations of normally solvable nonlinear operators, I |
| title_short | Perturbations of normally solvable nonlinear operators, I |
| title_sort | perturbations of normally solvable nonlinear operators i |
| topic | solvability normal solvabitity inverse function theorems Ekeland's theorem contractor directions. |
| url | http://dx.doi.org/10.1155/S0161171285000266 |
| work_keys_str_mv | AT williamoray perturbationsofnormallysolvablenonlinearoperatorsi AT anitamwalker perturbationsofnormallysolvablenonlinearoperatorsi |