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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:
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


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