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On Ulam Stability of a Linear Difference Equation in Banach Spaces

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Abstract

We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation \(x_{n+2}=ax_{n+1}+bx_n,\) where \(\mathbb {K}\) is one of the fields \(\mathbb {R}\) or \(\mathbb {C},\)\(a,b \in \mathbb {K}\) and \((x_n)_{n\ge 0}\) is a sequence in a Banach space X over the field \(\mathbb {K}.\) In this way, we improve and complement some recent results on Ulam stability of the second-order linear difference equation with constant coefficients.

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Correspondence to Alina Ramona Baias.

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Communicated by Rosihan M. Ali.

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Baias, A.R., Popa, D. On Ulam Stability of a Linear Difference Equation in Banach Spaces. Bull. Malays. Math. Sci. Soc. 43, 1357–1371 (2020). https://doi.org/10.1007/s40840-019-00744-6

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  • DOI: https://doi.org/10.1007/s40840-019-00744-6

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