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The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 689-695 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34A12, 34C11, 34L30, 47H10, 47N20
Keywords: contraction principle; Cauchy problem 
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     author = {Mortici, Cristinel},
     title = {The distance between fixed points of some pairs of maps in {Banach} spaces and applications to differential systems},
     journal = {Czechoslovak Mathematical Journal},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a31/}
}
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Mortici, Cristinel. The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 689-695. http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a31/

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