半弱紧1-集压缩映射不动点的迭代序列

Iterative Sequence of a Fixed Point of Semi-weak Compact l-set Contractions Mappings.

本文证明了,序区间[y,Y]上递增半弱紧1-集压缩映射 T 的极小不动点x_* 和极大不动点 x~*,仍可用简单迭代序列逼近.即 x_*=lim(T^ny) n→·,x~*=lim(T^nY) n→∞.同时,还建立了另一迭代序列.

Let (E,P)be on Ordered Banach Space with a normal positive cone let [y,Y[(?)P be an order intervat and T:[y,Y]→P be a semi-weak compact 1-set-contraction.Suppose that y≤Ty,Y≥TY,then T has a minimal fixed point x_* and a maximal fixed point x~*,and x_* and x~* Can be computed iteratively by method x_*=lim(T^ny) n→· and x~*=lim(T^nY) n→∞, respectively.