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Some iterative recurrence formulas. (English) Zbl 0766.11007

The author proves a conjecture of N. J. Fine [J. Math. Anal. Appl. 113, 185-187 (1986; Zbl 0596.10011)] that for \(G(0)=0\), \(G(n)=n-[bG(G(n- 1))]\), \(n=1,2,\dots\), where \(0<b<1\) and \(a\) the unique positive root of \(bx^ 2+x-1\), \(\{G(n)-a_ n\}\) is bounded.

MSC:

11B37 Recurrences
40A99 Convergence and divergence of infinite limiting processes

Citations:

Zbl 0596.10011
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