부산대학교 도서관

Main result: Let $f\colon[0,1]\rightarrow[0,1]$ be continuous and let $A=(a_{nk})$ be a stable iteration matrix; then for any $x_1\in[0,1]$, the generalized iteration sequence $(v_n)$, $v_n=\sum_{k=1}^na_{nk}x_k$, $x_{n+1}=f(v_n)$, converges to a fixed point of $f$ on $[0,1]$. \par This generalizes a result of J. Reinermann [Studia Math. {\bf 32} (1969), 209--227; MR0303371 (46 \#2508)]. However, the authors seem to be unaware of the article by B. E. Rhoades [Trans. Amer. Math. Soc. {\bf 196} (1974), 161--176; MR0348565 (50 \#1063)], which contains this and other results along these lines.