2008
DOI: 10.2140/involve.2008.1.91
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Difference inequalities, comparison tests, and some consequences

Abstract: Difference inequalities, comparison tests, and some consequences We study the behavior of nonnegative sequences which satisfy certain difference inequalities. Several comparison tests involving difference inequalities are developed for nonnegative sequences. Using the aforementioned comparison tests, it is possible to determine the global stability and boundedness character for nonnegative solutions of particular rational difference equations in a range of their parameters.

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Cited by 13 publications
(11 citation statements)
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“…First, we shall remove the assumption gcd is a solution of Equation (6). So that no confusion arises, we label the sets of indices for Equation (6) I * b and I * B and reserve the usual notation for our original difference equation.…”
Section: Resultsmentioning
confidence: 99%
“…First, we shall remove the assumption gcd is a solution of Equation (6). So that no confusion arises, we label the sets of indices for Equation (6) I * b and I * B and reserve the usual notation for our original difference equation.…”
Section: Resultsmentioning
confidence: 99%
“…[7]. We set z m ¼ x mpþb for m [ N. As we have just shown, {z m } satisfies the following difference inequality,…”
Section: Some General Unboundedness Resultsmentioning
confidence: 99%
“…See Refs [3,7] for a discussion on the technique of boundedness by iteration. In the following theorem, we use the technique of iteration in order to obtain bounds for certain subsequences of the solutions which we study.…”
Section: Unboundedness By Iterationmentioning
confidence: 99%
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“…We now rename this subsequence and apply the methods used in [4]. We set = L for ∈ N. As we have just shown { } satisfies the following difference inequality,…”
Section: Theorem 31mentioning
confidence: 99%