Hyers-Ulam stability of the linear recurrence with constant coefficients

By Dorian Popa. 2005

100 citations recorded by the source corpus.

Let X be a Banach space over the field ℝ or ℂ, a1,...,ap ∈ ℂ, and (bn)n≥0) a sequence in X. We investigate the Hyers-Ulam stability of the linear recurrence xn+p = a1xn+p-1 + ⋯ + ap-1xn+1 + apxn + bn, n ≥ 0, where x0,x1,...,xp-1 ∈ X.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8917dd2131bb63f49394d66aa48d91699925a2b9

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In Algebra and Number Theory

1. Ioan A. Rus
2. Janusz Brzdek
3. Bing Xu
4. Dorian Popa
5. Krzysztof Cieplinski

In Applied Mathematics

1. Ioan A. Rus
2. Janusz Brzdek
3. Bing Xu
4. Dorian Popa
5. Krzysztof Cieplinski

In Mathematical Physics

1. Ioan A. Rus
2. Janusz Brzdek
3. Bing Xu
4. Krzysztof Cieplinski

Citations in the corpus

• REMARKS ON ULAM STABILITY OF THE OPERATORIAL EQUATIONS (2009, background): “) and for difference equations ([3], [4], [5], [23], [24],.”
• The Hyers–Ulam stability of nonlinear recurrences (2007, background): “In [6] (see also [7]) the problem of stability has been considered for recurrences in a Banach space X over a field K ∈ {R,C}.”
• On the Stability of a Functional Equation Associated with the Fibonacci Numbers (2014, unknown): “[3–14]).”
• Note on nonstability of the linear recurrence (2006, background): “The Hyers-Ulam stability of linear recurrence with constant coefficients, a discrete case of equations in a single variable, was investigated in [ 11 ], where the second author of the present paper has proved the following theorem.”