广义Lipschitz伪压缩映射黏滞迭代逼近方法的强收敛

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x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*.

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

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 reaping f:K→K,the sequence {x_n} is given by:For x_1∈K,x_(n+1)= (1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.It is shown,under appropriate conditions on the sequences of real numbers {α_n} and {β_n},that {x_n} strongly converges to some fixed point x~* of T whenever {z∈K;μ_n||x_n-z||~2=inf_(y∈Kμ_n)||x_n-y||~2}∩F(T)≠0.