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:

00114642 (print) 
ISSN:

15729141 (online) 
Volume:

56 
Issue:

2 
Year:

2006 
Pages:

689695 
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 $\Vert uv\Vert .$ 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:

20090924T11:37:02Z 
Last updated:

20200703 
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/s1058700500581 
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 quasipositive 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 
. 