Discrete Ou-Iang type inequalities (Q2711247)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Discrete Ou-Iang type inequalities |
scientific article |
Statements
25 February 2002
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Ou-Iang type inequalities
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stability
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discrete inequalities
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difference equations
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sublinear perturbations
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Discrete Ou-Iang type inequalities (English)
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If \( x, f : [0, \infty ] \to R^+ \) are continuous functions, \( c > 0 \) and NEWLINE\[NEWLINE x^2 (t) \leq c^2 + 2 \int_0^t f(s) x(s) ds , NEWLINE\]NEWLINE then \textit{Ou-Iang} proved in 1957 that necessarily NEWLINE\[NEWLINE x(t) \leq c + \int_0^t f(s) ds,\quad t \in [0, \infty). NEWLINE\]NEWLINE The authors of this paper study some discrete inequalities of this type and connexions with the stability of difference equations with sublinear perturbations are presented.
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