Hillam迭代的一点注记(英文)

A NOTE ON HILLAM'S ITERATION SCHEME

设ａ＜ｂ及ｆ：［ａ，ｂ］→［ａ，ｂ］是一个函数，称下述迭代：ｘｎ＋１＝（１－λ）ｘｎ＋λｆ（ｘｎ），ｘ０∈［ａ，ｂ］为Ｈｉｌａｍ迭代，其中０＜λ＜１．给出了Ｈｉｌａｍ定理的一个简单证明，还得到了Ｈｉｌａｍ定理在无穷维空间ｌｐＲ中的一个推广形式．

Let a <b and f: → be a function. The following iteration scheme:xn+1=(1-λ)xn+λf(xn),xo∈is called to be Hillam's iteration scheme,where 0<λ<1.A simple proof to Hillam's Theorem is given and a generalization of Hillam's Theorem to infinite dimension is also obtained.