Banach空间中集值局部严格伪压缩映射的Ishikawa迭代过程

The Ishikawa Process for Local Strictly Pseudo-contractive Mapping in Banach Spaces

设X是一致光滑的Banach空间,T∶D(T)X→2X是局部严格伪压缩映射且有不动点.设Q是从X到D(T)上的非扩张保核映射.任取x0∈D(T)归纳定义xn+1=Qpn,pn∈(1-cn)xn+cnTQyn,yn∈(1-dn)xn+dnTxn.如果存在有界序列{wn}和{zn},wn∈TQyn,zn∈Txn.则{xn}强收敛于T的唯一不动点.其中数列{cn}和{dn}满足适当条件.

Let X be a real uniformly smooth Banach space, T ： D（T） belong to X→2^x be local strictly pseudo-contractive with a fixed point x^＊∈D（T）. Suppose there exists a nonexpansive retraction Q of X onto D（T）. Let the sequence {xn} be generated from arbitrary x0∈D（T） by xn＋1=Qpn, pn∈（1-cn）xn＋cnTQyn, yn∈（1-dn）xn＋dnTxn. Then {xn} converges strongly to the unique fixed point of T, provided that there exist bounded selections {wn} and {zn} with wn∈TQyn, zn∈Txn, and the sequence {cn} and {dn} satisfying appropriate conditions.