非扩张映象不动点的黏性逼近

Viscosity Approximation Fixed Points For Nonexpansive Mapping

设C是一致光滑Banach空间X的一个闭凸子集,T:C→C是非扩张映象且不动点集F(T)≠Φ,f:C→C是一个固定的压缩映射.序列{xn}由下式定义:xn+1=αnf(xn)+(1-αn)(βnxn+(1-βn)Txn)其中αn,βn∈(0,1).当αn和βn满足一定条件时,则序列{xn}强收敛到T的不动点.

Let C be a closed convex subset of a uniformly smooth Banach space X,and T：C→C is a non-expansive mapping such that,and be a fixed contractive mapping.The sequence is given by：xn＋1=αnf（xn）＋（1-αn）（βnxn＋（1-βn）Txn） where αn,βn∈（0,1）.We prove that{xn}strongly converges to a fixed point of T as αn,βn satisfying some appropriate conditions.