有限簇L-Lipschitzian映象的迭代程序

Iteration Process for a Finite Family of L-Lipschitzian Mappings

设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,+∞),limn→∞kn=1的有限簇一致L-Lipschitzian渐近伪压缩映象,且∩Ni=1F(Ti)≠Φ.设序列{xn}定义为xn+1=(1-αn-βn)xn+αnf(xn)+βnTnrnxn,其中{αn},{βn}[0,1],rn=nmodN是值域为{1,2,…,N}的模函数.在一定条件证明了迭代序列{xn}强收敛于T1,T2,…,TN的公共不动点.推广和改进了张石生等人的最新结果.

Let E bean areal Banach space, K bean nonempty closed convexsubset of E. Let f： K→ K bean aractive mapping, ,T1,T2,…,TN：K→K be a finite family of uniformly L - Lipschitzian asymptotically docontractive mappings with sequence {κn}belong to [1,＋∞）,lim（n→∞） κn=1 such that the set ^N∩i=1F（Ti）≠Ф Let {xn} be the iterative sequence defined by n＋1=（1-αn-βn）xn＋αnf（xn）＋βnT^n rn xn where{αn},{βn}belong to [0,1]and rn=n mod N,with the rood function takes values in the set {1,2,…,N} It is shown that under some suitable conditions, the iterafive sequence {xn}converges strongly to some fixedts of于T1,T2,…,TN. The resuits extend and improve some recent.