Short proof of a discrete Gronwall inequality (Q1088079)
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scientific article; zbMATH DE number 3989990
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Short proof of a discrete Gronwall inequality |
scientific article; zbMATH DE number 3989990 |
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Short proof of a discrete Gronwall inequality (English)
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1987
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In the classical discrete Gronwall inequality \(\{x_ n\leq a_ n+\sum^{n-1}_{j=n_ 0}b_ jx_ j,\quad n=n_ 0,...,N\quad implies\quad x_ n\leq a^*\prod^{n-1}_{j=n_ 0}(1+b_ j)\}\) the description of the multiplier \(a^*\) is improved and the use of such inequality in stability considerations for difference equations is illustrated.
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discrete Gronwall inequality
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multiplier
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stability
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difference equations
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