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• W2051744090 abstract "We consider the asymptotic behavior of bounded solutions of the difference equations of the form $x(n+1)=Bx(n) + y(n)$ in a Banach space $mathbb {X}$, where $n=1,2,...$, $B$ is a linear continuous operator in $mathbb {X}$, and $(y(n))$ is a sequence in $mathbb {X}$ converging to $0$ as $nto infty$. An obtained result with an elementary proof says that if $sigma (B) cap { |z|=1} subset { 1}$, then every bounded solution $x(n)$ has the property that $lim _{nto infty } (x(n+1)-x(n)) =0$. This result extends a theorem due to Katznelson-Tzafriri. Moreover, the techniques of the proof are furthered to study the individual stability of solutions of the discrete system. A discussion on further extensions is also given." @default.
• W2051744090 created "2016-06-24" @default.
• W2051744090 creator A5075591089 @default.
• W2051744090 date "2009-09-01" @default.
• W2051744090 modified "2023-10-05" @default.
• W2051744090 title "Asymptotic behavior of individual orbits of discrete systems" @default.
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• W2051744090 doi "https://doi.org/10.1090/s0002-9939-09-09871-2" @default.
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