2004
DOI: 10.1016/j.jmaa.2003.09.046
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Abstract: In this paper we study the boundedness and the asymptotic behavior of the positive solutions of the system of difference equations

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Cited by 19 publications
(14 citation statements)
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“…aÞð1 2 cÞj ; from which along with(26) and(27) these results easily follow. (e) By some simple calculation we have thata ð1Þ m ¼ ðb þ ðu i22 ð1 2 aÞ 2 bÞa m2iþ1 Þðd þ ðv 2i21 ð1 2 cÞ 2 dÞc m Þ ð1 2 aÞð1 2 cÞ ¼ 1 þ ðu i22 ð1 2 aÞ 2 bÞ b a m2iþ1 þ ðv 2i21 ð1 2 cÞ 2 dÞ d c m þ Oða m c m Þ; and b ð1Þ m ¼ ðd þ ðv i22 ð1 2 cÞ 2 dÞc m2iþ1 Þðb þ ðu 2i21 ð1 2 aÞ 2 bÞa m Þ ð1 2 aÞð1 2 cÞ ¼ 1 þ ðu 2i21 ð1 2 aÞ 2 bÞ b a m þ ðv i22 ð1 2 cÞ 2 dÞ d c m2iþ1 þ Oða m c m Þ; from which the convergence of the sequences ð Q m s¼0 a ð1Þ s Þ m[N 0 and ð Q m s¼0 b ð1Þ s Þ m[N 0 ; and consequently the convergence of the sequences ðx 2m2i Þ m[N and ðy 2m2i Þ m[N from formulas (26) and (27) easily follows.…”
supporting
confidence: 56%
“…aÞð1 2 cÞj ; from which along with(26) and(27) these results easily follow. (e) By some simple calculation we have thata ð1Þ m ¼ ðb þ ðu i22 ð1 2 aÞ 2 bÞa m2iþ1 Þðd þ ðv 2i21 ð1 2 cÞ 2 dÞc m Þ ð1 2 aÞð1 2 cÞ ¼ 1 þ ðu i22 ð1 2 aÞ 2 bÞ b a m2iþ1 þ ðv 2i21 ð1 2 cÞ 2 dÞ d c m þ Oða m c m Þ; and b ð1Þ m ¼ ðd þ ðv i22 ð1 2 cÞ 2 dÞc m2iþ1 Þðb þ ðu 2i21 ð1 2 aÞ 2 bÞa m Þ ð1 2 aÞð1 2 cÞ ¼ 1 þ ðu 2i21 ð1 2 aÞ 2 bÞ b a m þ ðv i22 ð1 2 cÞ 2 dÞ d c m2iþ1 þ Oða m c m Þ; from which the convergence of the sequences ð Q m s¼0 a ð1Þ s Þ m[N 0 and ð Q m s¼0 b ð1Þ s Þ m[N 0 ; and consequently the convergence of the sequences ðx 2m2i Þ m[N and ðy 2m2i Þ m[N from formulas (26) and (27) easily follows.…”
supporting
confidence: 56%
“…Consider system (4) where a 1 , a 2 , a 3 , b 1 , b 2 , b 3 are real numbers and the initial values are real numbers. Assume that (33), (34) hold and…”
Section: Proposition 32mentioning
confidence: 99%
“…We would like to point out that some of these papers study even some more general systems of difference equations which are nowadays frequently called close‐to‐cyclic (for the case of two‐dimensional system they are called close‐to‐symmetric, see, for example, other works). For some results on symmetric and close‐to‐symmetric systems, which are nowadays popular, see previous studies and the references therein. Finally, since difference equations have several applications in applied sciences, there exists an extended bibliography concerning theory and applications (see other works ),.…”
Section: Introductionmentioning
confidence: 99%
“…In [14], Papaschinopoulos and Schinas considered the system of difference equations x n+1 = A + y n x n-p , y n+1 = A + x n y n-q , n = 0, 1, . .…”
Section: Introductionmentioning
confidence: 99%