# Article

 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 .

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