强收敛于Banach空间中非扩张映象的切萨罗平均  

Strong Convergence to Cesro Means for Non-expansive Mappings in Banach Spaces

作　　者：刘敏[1] 左平[1] 

机构地区：[1]宜宾学院数学系,四川宜宾644000

出　　处：《南昌大学学报（理科版）》2010年第4期337-340,345,共5页Journal of Nanchang University(Natural Science)

基　　金：四川省教育厅重大培养项目(07zz046)

摘　　要：设f是一个压缩常数为h的压缩映象,T是一个非扩张映象使得F(T)≠Φ。{xn}是由下式xn+1=αnf(xn)+(1-αn)1/n+1 sum Tjxn from j=0 to n,n∈N,定义的迭代序列,其中{αn}(0,1)且满足lim αn=0 n→∞和sum αn=∞ from n=1 to ∞。证明{xn}强收敛于F(T)中某个变分不等式的唯一解。结果改进了Xu,Shimizu-Takahashi和Shioji-Takahashi的主要结果。Let f be a fixed contraction with contractive constant h and T be a non-expansive mapping with F（T）≠Φ.The sequence {xn} is iteratively defined as follows. xn＋1=αn f（xn）＋（1-αn）1/n＋1 sum Tjxn from j=0 to n,n∈N,where {αn}（0,1） satisfies the conditions lim αn = 0 n→∞and sum αn=∞ from n=1 to ∞.It proves that {xn } converges strongly to the unique solution x~ to some variational inequality in F（T）.Our results improve the main results in Xu,Shimizu-Takahashi and Shioji-Takahashi.

关 键 词：非扩张映象 切萨罗平均 变分不等式 正规对偶映象 

分 类 号：O177[理学—数学]