On contractions in $L_1$
نویسندگان
چکیده
منابع مشابه
$L_1/\ell_1$-to-$L_1/\ell_1$ analysis of linear positive impulsive systems with application to the $L_1/\ell_1$-to-$L_1/\ell_1$ interval observation of linear impulsive and switched systems
Sufficient conditions characterizing the asymptotic stability and the hybrid L1/`1-gain of linear positive impulsive systems under minimum and range dwell-time constraints are obtained. These conditions are stated as infinite-dimensional linear programming problems that can be solved using sum of squares programming, a relaxation that is known to be asymptotically exact in the present case. The...
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where \p is some function defined on the closure of the range of p. In [3], Rakotch proved that if \p(t) =ct(t)t, where a is decreasing and a(t) <1 for i>0, then a mapping satisfying (3) has a unique fixed point x0. It is an easy exercise to show that if \p(t) =a(t)t, where a is increasing, and a(/)<l for t^O, then the conclusion of Banach's theorem still holds. We shall show that one need only...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1989
ISSN: 0528-2195
DOI: 10.21136/cpm.1989.118384