严格伪压缩映象的复合隐格式迭代序列的收敛率估计

Convergence Rate Estimate of Composite Implicite Iteration Method for Strictly Pseudocontractive Maps

设K是实Banach空间E的非空闭凸集,{Ti}iN=1:K→K是N个严格伪压缩映象且公共不动集F=∩Ni=1F(Ti)≠φ,其中F(Ti)={x∈K:Tix=x}.{αn}n∞=1,{βn}n∞=1[0,1]是实序列且满足条件:(i)sum from n=1 to ∞ (αn)(ii)lim(n→∞)αn=lim(n→∞)βn=0(iii)αnβnL2<1,n≥1其中L≥1是{Ti}iN=1的公共Lipschitz常数.对于任意的x0∈K,设{xn}n∞=1是由下列产生的复合隐格式迭代序列:xn=(1-αn)xn-1+αn Tnynyn=(1-βn)xn-1+βnTnxn其中Tn=Tn mod N,则{xn}强收敛到{Ti}iN=1的公共不动点.结果推广和改进了相关文献的结果,且主要定理的证明方法也是不同的.并且进一步给出了序列的收敛率估计.

Abstract ： Let E be a real Banach space and let K be a nonempty closed convex subset of E. Let{T1},n^N=1be N strictly pseudocontractive self-maps of K such rhat F=i-1∩^NF（T）≠Фwhere F（T1）={x∈K：T,x=x},{an}n=n^∞,{βn}n=1^∞∈[0,1]be real sequence satisfying the conditions（i）n=1∑^∞an=∞（ii）liman a=∞=limn=∞βn=0（iii）anβnL^2〈1,n≥1 is common Lipschitz constant of{（Ti}^N=1F orx0∈K let{xn}n^∞=1be defined by,xn=（1-αn）xn-1＋αnTnyn yn=（1-β）xn-1＋βnTnxnwhereTn=Tn med N.,thenXm}converges strongly to common fixed point of{T1}1^N=1 The results gernalize and improve the results of correlation literature, and the methods of ＂ proof of main results are also different. Furthermore, we give convergence rate estimate of the iterative sequence in this paper.