| Title:
|
Weakly coercive mappings sharing a value (English) |
| Author:
|
Soriano, J. M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
65-72 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some sufficient conditions are provided that guarantee that the difference of a compact mapping and a proper mapping defined between any two Banach spaces over $\mathbb {K}$ has at least one zero. When conditions are strengthened, this difference has at most a finite number of zeros throughout the entire space. The proof of the result is constructive and is based upon a continuation method. (English) |
| Keyword:
|
zero point |
| Keyword:
|
continuation method |
| Keyword:
|
$C^{1}$-homotopy |
| Keyword:
|
surjerctive implicit function theorem |
| Keyword:
|
proper mapping |
| Keyword:
|
compact mapping |
| Keyword:
|
coercive mapping |
| Keyword:
|
Fredholm mapping |
| MSC:
|
47J07 |
| MSC:
|
58C15 |
| MSC:
|
58C30 |
| MSC:
|
65H10 |
| MSC:
|
65J15 |
| idZBL:
|
Zbl 1224.58008 |
| idMR:
|
MR2782759 |
| DOI:
|
10.1007/s10587-011-0017-y |
| . |
| Date available:
|
2011-05-23T12:30:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141518 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Alexander, J. C., York, J. A.: Homotopy Continuation Method: numerically implementable topological procedures.Trans. Amer. Math. Soc. 242 (1978), 271-284. MR 0478138, 10.1090/S0002-9947-1978-0478138-5 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Soriano, J. M.: Continuous embeddings and continuation methods.Nonlinear Anal. Theory Methods Appl. 70 (2009), 4118-4121. Zbl 1176.58005, MR 2515328, 10.1016/j.na.2008.08.015 |
| Reference:
|
[9] Zeidler, E.: Nonlinear Functional Analysis and its applications I.Springer-Verlag, New York (1992). MR 0816732 |
| Reference:
|
[10] Zeidler, E.: Applied Functional Analysis.Springer-Verlag, Applied Mathematical Sciences 109, New York (1995). Zbl 0834.46002, MR 1347691, 10.1007/978-1-4612-0821-1_3 |
| . |
