严格伪压缩映像族不动点的隐格式组迭代逼近

System of implicit iteration for fixed points of a finite family of strictly pseudocontractive mappings

设E是实Banach空间,K是E中非空闭凸集,{Ti}i=1N是K中严格伪压缩映像族,对x0∈K,一个新的隐迭代格式组按如下格式给出:xn=αnxn-1+(1-αn)Tnyn yn=βnxn-1+(1-βn)Tnxn 这里Tn=TnmodN,{αn},{βn}(?)[0,1],n≥1．该文研究这个新格式逼近严格伪压缩映像族不动点问题．证明了序列{xn}可以逼近严格伪压缩映像族{Ti}i=1N的不动点．

Let E be real Banach space and K a nonempty convex subset of E, and let {Ti}i=1^N be a finite family of Strictly pseudocontractive self-maps of K, for x0 ∈ K, a new system of implicit iteration process is put forward as following xn=αnxn-1＋（1-αn）Tnyn yn=βnxn-1＋（1-βn）Tnxn Where Tn=TnmodN,n≥1,{αn},{βn} belong to [0,1]. The problems of approximating fixed points of strictly pseudcontractive mappings in an arbitrary real Banach spaces by this new interation sequence is investigated. Meanwhile, strong convergent theorems are also proved.