有限簇L-Lipschitzian渐近伪压缩映象的收敛定理  

Convergence Theorem for a Finite Family of L-Lipschitzian Asymptotically Pseudocontractive Mappings

作　　者：徐天华[1] 

机构地区：[1]四川民族学院数学系,四川康定626001

出　　处：《广西民族大学学报（自然科学版）》2010年第3期70-74,共5页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：四川民族学院资助项目(2009[8])

摘　　要：E是一实Banach空间,K是E的一非空闭凸子集.设f:K→K是一压缩映象,T1,T2…,TN∶K→K是具序列{kn}[1,+∞),lim kn=1 n→∞的有限簇一致L-Lipschitzian渐近伪压缩映象,且∩F(Ti)≠Φ from i=1 to N.设序列{xn}定义为xn+1=(1-αn-βn)xn+αnf(xx)+βnTrnnyn yn=(1-γn)xn+γnTrnnxn,n≥0其中{αn},{βn},{γn}[0,1],rn=n mod N.文章在一定条件下,用黏性逼近法证明了迭代序列{xn}强收敛于T1,T2,…,TN的公共不动点.该文结果推广和改进了一些文献的最新结果.Let E be a real Banach space,K be a nonempty closed convex subset of E.Let f：K→K be a contractive mapping,T1,T2,…,TN∶K→K be a finite family of uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}[1,＋∞）,lim kn=1 n→∞ such that the set ∩F（Ti）≠Φ from i=1 to N.Let{xn} be the iterative sequence defined by xn＋1=（1-αn-βn）xn＋αnf（xx）＋βnTnrnynyn=（1-γn）xn＋γnTnrnxn n≥0,Where {αn},{βn},{γn}[0,1] and rn= n mod N.It is shown that under some suitable conditions by viscosity approximation methods,the iterative sequence {xn}converges strongly to some fixed points of T1,T2,…,TN.The results presented in the paper extend and improve some recent results.

关 键 词：一致L-Lipschitzian映象 渐近伪压缩映象 黏性逼近 正规对偶映象 不动点 

分 类 号：O177.91[理学—数学]