连续伪压缩映射的黏滞迭代逼近方法

Viscosity Approximation Methods for Continuous Pseudocontractive Mappings

设K是实自反Banach空间E的一个闭凸子集，T：K→K是一个连续伪压缩映射，f：K→K是一个固定的L—Lipschitzian强伪压缩映射．对于任意的t∈（0，1），设Xt是tf＋（1-t）T的唯一不动点．我们证明了如果T有不动点且有从E到E^＊弱序列连续对偶映像，则当t趋于0时，{xt}收敛于T的一个不动点．这个结果改进和推广了文[4]的相应结果．

Let K be a closed convex subset of a real reflexive Banach space E, T ： K → K be a continuous pseudocontractive mapping, and f ： K → K be a fixed L-Lipschitzian strongly pseudocontractive mapping. For any t∈ （0, 1）, let xt be the unique fixed point of tf ＋ （1 - t）T. We prove that if T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then （xt） converges to a fixed point of T as t approaches 0. The results presented extend and improve the corresponding results of [4].