| Title:
|
The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems (English) |
| Author:
|
Mortici, Cristinel |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
689-695 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $T$ be a $\gamma $-contraction on a Banach space $Y$ and let $S$ be an almost $\gamma $-contraction, i.e. sum of an $\left( \varepsilon ,\gamma \right) $-contraction with a continuous, bounded function which is less than $\varepsilon $ in norm. According to the contraction principle, there is a unique element $u$ in $Y$ for which $u=Tu.$ If moreover there exists $v$ in $Y$ with $v=Sv$, then we will give estimates for $\Vert u-v\Vert .$ Finally, we establish some inequalities related to the Cauchy problem. (English) |
| Keyword:
|
contraction principle |
| Keyword:
|
Cauchy problem |
| MSC:
|
34A12 |
| MSC:
|
34C11 |
| MSC:
|
34L30 |
| MSC:
|
47H10 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1164.47358 |
| idMR:
|
MR2291767 |
| . |
| Date available:
|
2009-09-24T11:37:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128097 |
| . |
| Reference:
|
[1] C. Mortici: Approximate methods for solving the Cauchy problem.Czechoslovak Math. J. 55 (2005), 709–718. MR 2153095, 10.1007/s10587-005-0058-1 |
| Reference:
|
[2] C. Mortici and S. Sburlan: A coincidence degree for bifurcation problems.Nonlinear Analysis, TMA 53 (2003), 715–721. MR 1959568 |
| Reference:
|
[3] C. Mortici: Operators of monotone type and periodic solutions for some semilinear problems.Mathematical Reports 54 (1/2002), 109–121. MR 1994122 |
| Reference:
|
[4] C. Mortici: Semilinear equations in Hilbert spaces with quasi-positive nonlinearity.Studia Cluj. 4 (2001), 89–94. Zbl 1027.47044, MR 1989718 |
| Reference:
|
[5] D. Pascali and S. Sburlan: Nonlinear Mappings of Monotone Type.Alphen aan den Rijn, Sijthoff & Noordhoff International Publishers, The Netherlands, 1978. MR 0531036 |
| Reference:
|
[6] S. Sburlan, L. Barbu and C. Mortici: Ecuaţii Diferenţiale.Integrale şi Sisteme Dinamice. Editura Ex Ponto, Constanţa, Romania, 1999. MR 1734289 |
| . |
