Feng, Keqin Some iterative recurrence formulas. (English) Zbl 0766.11007 J. China Univ. Sci. Technol. 19, No. 3, 280-290 (1989). 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 PDFBibTeX XMLCite \textit{K. Feng}, J. China Univ. Sci. Technol. 19, No. 3, 280--290 (1989; Zbl 0766.11007)