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We obtain some results on Ulam stability for the linear difference equation $$x_{n+1}=a_nx_n+b_n,\, n\geq0$$ , in a Banach space X. If there exists $$\lim_{n\to\infty}|a_n|=\lambda$$ , then the equation is Ulam… Click to show full abstract
We obtain some results on Ulam stability for the linear difference equation $$x_{n+1}=a_nx_n+b_n,\, n\geq0$$ , in a Banach space X. If there exists $$\lim_{n\to\infty}|a_n|=\lambda$$ , then the equation is Ulam stable if and only if $$\lambda\neq 1$$ . Moreover if $$(|a_n|)_{n\geq 0}$$ is a monotone sequence, then the best Ulam constant of the equation is $$\frac{1}{|\lambda-1|}$$ .
Keywords:
linear difference;
best ulam;
difference equation;
equation;
ulam constant
Journal Title: Acta Mathematica Hungarica
Year Published: 2020
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Journal Title: Acta Mathematica Hungarica
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!