| Title:
|
A Common Fixed Point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces (English) |
| Author:
|
Akkouchi, Mohamed |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
5-15 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the setting of a b-metric space (see [Czerwik, S.: Contraction mappings in b-metric spaces Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.] and [Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276.]), we establish two general common fixed point theorems for two mappings satisfying the (E.A) condition (see [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.]) under strict expansive conditions using two classes of implicit relations. These two theorems may be considered as extensions of the main result of [Popa, V.: A General fixed point theorem for expansive mappings under strict implicit conditions Stud. Cerc. St. Ser. Mat. Univ. Bacău 17 (2007), 197–200.] to b-metric spaces. Also, the main result of [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math. Anal. Appl. 270 (2002), 181–188.] is obtained as a consequence of our results. (English) |
| Keyword:
|
common fixed point |
| Keyword:
|
metric space |
| Keyword:
|
b-metric space |
| Keyword:
|
property (E.A) |
| Keyword:
|
implicit relation |
| Keyword:
|
expansive mapping |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1246.54035 |
| idMR:
|
MR2920694 |
| . |
| Date available:
|
2011-12-08T09:42:56Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141716 |
| . |
| Reference:
|
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| Reference:
|
[2] Czerwik, S.: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11. Zbl 0849.54036, MR 1250922 |
| Reference:
|
[3] Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces. Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276. Zbl 0920.47050, MR 1665883 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| . |
