严格伪压缩映象的复合隐格式迭代序列的收敛率估计

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.

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

Let E be a real Banach space and let K be a nonempty closed convex subset of E. Let {Ti}Ni=1 be N strictly pseudocontractive self-maps of K such that F=∩Ni=1F(Ti)≠φ, where F(Ti)={x∈K:Tix=x}, and let {αn}∞n=1,{βn}∞n=10,1] be real sequence satisfying the conditions:(i)sum from n=1 to ∞(αn) (ii)lim(n→∞)αn=lim(n→∞)βn=0 (iii) αnβnL2<1,n≥1where L≥1is common Lipschitz constant of {Ti}Ni=1. F or x0∈K, let {xn}∞n=1 be defined by,xn=(1-αn)xn-1+αnTnynyn=(1-βn)xn+βnTnxnwhere Tn=Tn mod N, then {xn} converges strongly to common fixed point of {Ti}Ni=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.