Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients
2015 ◽
Vol 2015
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pp. 1-5
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Keyword(s):
We study the Hyers-Ulam stability in a Banach spaceXof the system of first order linear difference equations of the formxn+1=Axn+dnforn∈N0(nonnegative integers), whereAis a givenr×rmatrix with real or complex coefficients, respectively, and(dn)n∈N0is a fixed sequence inXr. That is, we investigate the sequences(yn)n∈N0inXrsuch thatδ∶=supn∈N0yn+1-Ayn-dn<∞(with the maximum norm inXr) and show that, in the case where all the eigenvalues ofAare not of modulus 1, there is a positive real constantc(dependent only onA) such that, for each such a sequence(yn)n∈N0, there is a solution(xn)n∈N0of the system withsupn∈N0yn-xn≤cδ.
2006 ◽
Vol 320
(2)
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pp. 549-561
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Keyword(s):
2015 ◽
Vol 47
(4)
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pp. 636-649
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Keyword(s):