无限簇非扩张非自映象公共不动点的黏性逼近法

Viscosity Approximation Methods for Common Fixed Points of Infinite Nonexpansive Nonself-mappings

设E是具有一致Gateaux可微范数的严格凸的自反的Banach空间,K是E的非空闭凸子集而且是E的sunny非扩张收缩核.设f：K→K是一压缩映象,P：E→K是一sunny非扩张保核收缩,{Tn}n∞1：K→E是一可数无限簇非扩张非自映象且是[0,1]中的非负数列.考虑下列迭代序列其中Wn是由P,Tn,T（n-1）,…,T1和λn,λ（n-1）,…,λ1,n≥1生成的W-映象.该文在较弱条件下用黏性逼近方法证明了迭代序列{x_n}强收敛于p∈F且p是下列变分不等式〈（I-f）p,j（p-x＊）〉≤0,x＊∈F的唯一解.

Let E be a real strictly convex and reflexive Banach space with a uniformly Gateaux differentiable norm and K be a nonempty closed convex subset of E which is also a sunny non- expansive retract of E. Let f：K→K be a contractive mapping, P be a sunny nonexpansive T retraction of E onto K and { n}n=1 ： K → E be a family of countable infinite nonexpansive nonself-mappings such that the common fixed point set seqence of nonnegative numbers in [0, 1]. Consider the following iterative sequence where Wn is the W-mapping generated by P, Tn,Tn-1,… ,T1 and λn,λ（n-1）,…,λ1,n≥1 for any n ≥ 1. It is shown that under very mild conditions on the parameters, the sequence {Xn} converges strongly to p C F, where p is the unique solution in F to the following variational inequality 〈（I-f）p,j（p-x＊）〉≤0,x＊∈F