A part-metric-related inequality chain and application to the stability analysis of difference equation

作者：Yang Xiaofan^*; Yang Maobin; Liu Huaiyi

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2007, 2007: 19618.

DOI：10.1155/2007/19618

We find a new part-metric-related inequality of the form min{a(i), 1/a(i) : 1 <= i <= 5} <= ((1+ w) a(1)a(2)a(3) + a(4) + a(5))/(a(1)a(2) + a(1)a(3) + a(2)a(3) + wa(4)a(5)) = max{a(i), 1/a(i) : 1 <= i <= 5}, where 1 <= w <= 2. We then apply this result to show that (c) over cap = 1 is a globally asymptotically stable equilibrium of the rational difference equation x(n) = (x(n-1) + x(n-2) +(1+w) x(n-3)x(n-4)x(n-5))/ (wx(n-1)x(n-2) + x(n-3)x(n-4) + x(n-3)x(n-5) + x(n-4)x(n-5)), n = 1, 2,..., a(0), a(-1), a(-2), a(-3), a(-4) > 0.

• 出版日期2007
• 单位重庆大学