广义Lipschitz伪压缩映射黏滞迭代逼近方法的强收敛

Strong Convergence Theorems of Viscosity Approximation Methods for Generalized Lipschitz Pseudocontractiive Mappings

K是Banach空间E的一个非空闭凸子集,T：K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f：K→K和x1∈K,序列{xn}由下式定义：xn＋1=（1-αn-βn）xn＋αnf（xn）＋βnTxn.在{αn}与{βn}满足合适条件的情况下,每当{z∈K;μn‖xn-z‖^2=inf（y∈K）μn‖xn-y‖^2}∩F（T）≠Ф时,{xn}强收敛到T的某个不动点x^＊.

Let K be a nonempty closed convex subset of Banach space E, and T ： K → K be a generalized Lipschitz pseudocontractive mapping. For any fixed Lipschitz strong pseudocontractive maping f ： K → K, the sequence {xn} is given by： For x1∈K, xn＋1 = （1 -αn-βn）xn＋αn,αnf（xn）＋βnTxn. It is shown, under appropriate conditions on the sequences of real numbers {αn } and {βn }, that {xn } strongly converges to some fixed point x^＊ of T whenever{z∈K;μn‖xn-z‖^2=inf（y∈K）μn‖xn-y‖^2}∩F（T）≠Ф.